| ab�ndern | vt | ~ in + acc. - to alter (to), to revise (to)
|
| Abb. | abbr | (= Abbildung�)
|
| abbilden | vt | to map
|
| Abbildung� | f | mapping, function
|
| Abbildung� | f | illustration, diagram
|
| abelsche Gruppe | | abelian group
|
| aber | conj | but
|
| abge�ndert | vb | pp of ab�ndern
|
| abgeschlossen | adj | closed, algebraisch ~ - algebraically closed
|
| abgeschlossene H�lle | | closure
|
| abh�ngen | vi | ~ von - depend (on)
|
| abh�ngig | adj | ~ von - dependent on
|
| abh�ngt | vb | tps of abh�ngen
|
| abk�rzen | vt | to shorten, to abbreviate
|
| Abk�rzung | f | abbreviation
|
| ableiten | vt | to deduce, to derive
|
| Ableitung | f,-en | derivative, deduction, derivation
|
| abnehmen | vt | to decrease
|
| Abri� | m,-sse | outline
|
| Absch�tzung | f | estimation, assessment
|
| Abschlie�ung | f | closure
|
| Abschnitt | m | section, segment
|
| absolut regul�r | | absolutely regular
|
| abspalten | vt | to split off
|
| Abspaltung | f | splitting-off
|
| Abstand | m | distance
|
| absteigend | adj | descending
|
| abstrakt | adj | abstract
|
| abstrakt | adv | abstractly
|
| abz�hlbar | adj | countable, denumerable
|
| Achse | f,-n | axis
|
| addieren | vt | to add
|
| Addition | f | addition
|
| Additivit�t | f | additivity
|
| affine | adj | affine
|
| �hnlich | adj | (+ dat.) similar (to)
|
| Algebra | f,- | algebra
|
| algebraisch | adj | algebraic, ~ abgeschlossen - algebraically closed
|
| algebraische Zahl | | algebraic number
|
| algebraische Zahlentheorie | | algebraic number theory
|
| Algorithmus | m,-men | algorithm
|
| alle(r,s) | adj | all, f�r alle - for all
|
| allerdings | adv | however, certainly, admittedly
|
| allgemein | adj | general
|
| allgemeiner | adv | more generally
|
| als | prep | as, than
|
| alternierende Gruppe | | alternating group
|
| analog | adj | analogous
|
| analog | adv | analogously
|
| Analogie | f | analogy
|
| andere(r,s) | adj | other, different, mit anderen Worten - in other words
|
| andererseits | adv | on the other hand
|
| �ndern | vt | to alter, to change
|
| andernfalls | adv | otherwise
|
| anders | adv | ~ als - differently (from)
|
| anders ausgedr�kt | | in other words
|
| anders gesagt | | in other words
|
| angeben | vt | to give
|
| angenommen | adj | assumed
|
| angenommen | vb | pp of annehmen
|
| Angriff | m | etw in ~ nehmen - to make a start on sth
|
| anhand | prep | (+ gen.) with, through
|
| Anhang | m | appendix
|
| Anleitung | f | hint, instruction
|
| anmerken | vt | to observe
|
| Anmerkung | f | note
|
| annehmen | vt | to assume, suppose
|
| annulieren | vt | to annihilate
|
| Annullator | m,-en | annihilator
|
| anordnen | vt | to arrange
|
| Ansatz | m | formulation, setup, equation
|
| anschaulig | adj | illustrative
|
| anschlie�end | adj | adjacent, subsequent
|
| ansonsten | adv | otherwise
|
| anwenden | vt | to use, employ, apply
|
| Anwendung | f | use, application
|
| Anzahl | f | number (of)
|
| Approximationstheorie | | approximation theory
|
| �quivalent | adj | equivalent
|
| �quivalenz | f,-en | equivalence
|
| �quivalenzklasse | f,-n | equivalence class
|
| �quivalenzrelation | | equivalence relation
|
| Art | f,-en | kind, type, sort, way
|
| artinsche | adj | Artinian
|
| assoziativ | adj | associative
|
| Assoziativgesetz | nt | associative law, allgemeines ~ - generalized associative law
|
| assoziieren | vt | to associate
|
| assoziiert | adj | associated
|
| auch | adv | also
|
| aufbauen | vt | ~ auf + dat - to base on
|
| auffassen | vt | to consider
|
| Aufgabe | f,-n | exercise, task, homework
|
| Auflage | f | edition
|
| aufl�sbare Gruppe | | solvable group
|
| Aufl�sung | f,-en | resolution
|
| aufsammeln | vt | to gather up
|
| Aufschlu� | m,�e | information
|
| aufspannen | vt | to span
|
| aufsteigend | adj | ascending
|
| aufteilen | vt | to divide up, to partition
|
| Aufteilung | f | division, partition
|
| auftreten | vi | to occur, to appear, to arise
|
| auftritt | vb | tps of auftreten
|
| aufwendig | adj | costly
|
| aufzufassen | vt | to consider
|
| aus | prep | from; of
|
| Ausdruck | m,�e | expression
|
| ausdr�cken | vt | to express
|
| Ausdrucksweise | f | terminology
|
| ausf�hrbar | adj | feasible
|
| ausf�hrlich | adj | detailed
|
| ausf�hrlich | adv | in detail
|
| Ausf�hrlichkeit | f | detail
|
| Ausgabe | f | output
|
| ausklammern | vt | to exclude, to factor out
|
| Auskunft | f,�e | information
|
| ausnutzen | vt | to use, to exploit
|
| ausrechnen | vt | to calculate
|
| ausreichen | vi | to suffice, to be enough
|
| Aussage | f,-n | statement
|
| au�erdem | conj | besides, in addition
|
| �u�erer Automorphismus | | outer automorphism
|
| au�erhalb | adv | outside
|
| au�erhalb | prep | (+ gen.) outside
|
| Austausch | m | exchange
|
| Auswahl | f | selection, choice
|
| auszeichnen | vr | to be charactrized by
|
| Automorphismengruppe | | automorphism group, group of automorphisms
|
| Automorphismus | m,-men | automorphism
|
| axiomatisch | adj | axiomatic
|
| Band | m,�e | volume (of a book)
|
| Basis | f,Basen | basis, base
|
| basisch | adj | basic
|
| Basisvektor | | basis vector
|
| beachten | vt | to note, to take into account
|
| Beachtung | f | notice, attention, observation
|
| beantworten | vt | to answer
|
| Bedarf | m | need, requirement
|
| bedeutend | adj | important, considerable
|
| Bedeutung | f | significance, importance, meaning
|
| Bedingung | f | condition
|
| befassen | vt | to concern, to treat
|
| beginnen | vi | to start, to begin
|
| Begriff | m,-e | concept; idea
|
| behandeln | vt | to treat, to deal with, to handle
|
| Behauptung | f | assertion, claim
|
| beide | pron,adj | both
|
| Beispiel | nt,-e | example
|
| beispielsweise | adv | for instance; for example
|
| bekannt | adj | well-known, familiar
|
| bekanntlich | adv | as is well-known
|
| beliebig | adj | arbitrary
|
| Bemerkung | f | remark
|
| ben�tigen | vt | to need
|
| benutzen | vt | to use
|
| ben�tzen | vt | to use
|
| beobachten | vt | to observe
|
| Beobachtung | f | observation
|
| bequem | adj | convenient
|
| berechnen | vt | to compute, to calculate
|
| Berechnung | f | computation
|
| bereits | adv | already
|
| ber�hren | vt | to meet, to intersect, to touch
|
| Ber�hrung | f | contact
|
| Ber�hrungspunkt | | point of contact
|
| besagen | vt | to mean
|
| beschleunigen | vt | to accelerate, to speed up
|
| beschr�nken | vt | to restrict
|
| Beschr�nkung | f | restriction (of a function)
|
| beschreiben | vt | to describe
|
| Beschreibung | f | description
|
| beschrieben | vb | pp of beschreiben
|
| besetzen | vt | to set, to occupy
|
| besitzen | vt | to possess, own, have
|
| besitzt | vb | pp of besitzen
|
| besonders | adv | especially, particularly
|
| besprechen | vt | to discuss
|
| besprochen | vb | pp of besprechen
|
| Bestandteil | nt | component
|
| Bestandteil | m | constitutent, material, part
|
| best�tigen | vt | to confirm, to establish
|
| best�tigt | vb | establishes
|
| bestehen | vi | to exist
|
| bestehen | vt | ~ aus - to consist of
|
| bestehend | adj | consisting of
|
| bestimmen | vt | to determine, to define, to specify
|
| Bestimmung | f | determining, purpose, definition
|
| beteiligen | vi | to take part
|
| beteiligt | adj | participating, involved
|
| betrachten | vt | to look at; to consider
|
| Betrachtung | f | observation; consideration
|
| betragen | vi | to amount to
|
| Betriebssystem | nt | operating system
|
| Bettireihe | f,-n | Betti series
|
| Bettizahlen | pl | Betti numbers
|
| Beweis | m,-e | proof
|
| beweisen | vt | to prove, to show
|
| Bewertung | f | valuation
|
| bewirken | vt | to cause, bring about, effect
|
| bezeichnen | vt | to denote, call, describe, indicate
|
| Bezeichnung | f | description, mark
|
| Beziehung | f | relation
|
| Bidualmodul | | bidual module
|
| bijektiv | adj | bijective
|
| Bild | nt,-er | image
|
| bilden | vt | to form, to constitute
|
| Bildung | f | formation
|
| Binomialtheorem | | binomial theorem
|
| bis auf | prep | up to
|
| bisher | adv | till now, hitherto
|
| bleiben | vi | to remain, to stay
|
| boolesche Algebra | | Boolean algebra
|
| Bruch | m,�e | fraction
|
| Buchband | m,�e | volume (of a book)
|
| Buchstabe | m,-n | letter (of the alphabet)
|
| buchstabieren | vt | to spell
|
| bzgl. | abbr | (= bez�glich) referring to (re.), concerning
|
| bzw. | abbr | (= beziehungsweise) or, that is, and ... respectively
|
| Ebene | f,-n | plane
|
| ebenfalls | adv | indeed
|
| ebenso | adv | just as
|
| echt | adj | proper (subset)
|
| echt monoton | | strictly monotonic
|
| Ecke | f,-n | angle
|
| effektiv | adj | effective, actual
|
| eigen | adj | own
|
| Eigenschaft | f,-en | property; attribute
|
| Einbettung | f | embedding
|
| Einbettungsdimension | | embedding dimension
|
| eindeutig | adj | unique
|
| Eindeutigkeit | f | uniqueness
|
| eineindeutig | adv | one-one, injective
|
| einfach | adj | simple
|
| einfach | adv | simply
|
| einfache Gruppe | | simple group
|
| einfacher Modul | | simple module
|
| einfacher Punkt | | simple point
|
| einf�hren | vt | to bring in; to introduce
|
| Einf�hrung | f | introduction
|
| Eingabe | f | input
|
| eingangs | adv | at the outset (beginning)
|
| eingangs | prep | (+ gen.) at the outset of
|
| eingebettet | adj | embedded
|
| eingef�hrt | vb | pp of einf�hren
|
| eingehen | vt | to enter (or go) into
|
| eingehend | adj | in-depth, thorough
|
| Einheit | f | unit (in a ring)
|
| Einheits-Gruppe | | the trivial group
|
| Einheitskreis | | unit circle
|
| Einheitswurzel | f,-n | root of unity
|
| einige(r,s) | adj,pron | some
|
| einige | pl | some, several
|
| Eins | | identity element (of a ring)
|
| einschieben | vt | to insert
|
| einschlie�lich | adv | including
|
| einschr�nkend | adj | restrictive
|
| Einschr�nkung | f | restriction, limitation
|
| Einselement | | identity element
|
| einsetzen | vt | substitute, enter, insert
|
| Einsetzung | f,-en | substitution, insertion
|
| einstellen | vt | to adjust, to set
|
| einstellig | adj | unary
|
| einzig | adj | single, only, unique
|
| Element | nt,-e | element
|
| elementar | adj | elementary
|
| Elementenzahl | | number of elements
|
| enden | vi | to end
|
| endlich | adj | finite
|
| endlich | adv | finitely
|
| endlich viel | | finitely many
|
| Endomorphismus | m,-men | endomorphism
|
| eng | adj | close, tight
|
| enorm | adj | enormous, tremendous
|
| entdecken | vt | to discover
|
| entgegen | prep | (+ dat) contrary to
|
| enth�lt | vb | contains
|
| enthalten | vt | to contain
|
| entscheiden | vt | to decide
|
| entsprechen | vi | to correspond to
|
| entsprechend | adj | appropriate, corresponding, suitable
|
| entsprechend | adv | accordingly
|
| entstehen | vi | ~ aus/durch - to arise from, to result from
|
| entwickeln | vt | to develop, to expand
|
| Entwicklung | f | explicit form, expansion, development
|
| Epimorphismus | m,-men | epimorphism
|
| erfinden | vt | to invent
|
| erf�llen | vt | to fulfil, to satisfy
|
| erf�llt | vb | pp of erf�llen
|
| Erg�nzung | f | completion, supplement
|
| ergeben | vr | (sich) ~ - to yield, to produce, to result, to arise, to follow
|
| Ergebnis | nt,-se | result
|
| erhalten | vt | to get, obtain, receive, preserve, conserve
|
| Erhaltung | f,-en | preservation, conservation
|
| erhoffen | vt | to hope for
|
| erh�hen | vt | to raise, to increase
|
| Erh�hung | f,-en | rise, increase
|
| erinnern | vt | ~ an + acc. - to remind (of), to recall
|
| erkennen | vt | to recognize, to see
|
| Erkenntnis | f,-se | knowledge, information, insight
|
| erkl�ren | vt | to explain
|
| erl�utern | vt | to explain
|
| erl�utert | vb | pp of erl�utern
|
| er�ffnen | vt | to open
|
| Ersatz | m | substitute
|
| ersetzen | vt | to replace, to substitute
|
| ersichtlich | adj | evident, obvious
|
| erste | adj | first
|
| erweitert | adj | extended
|
| Erweiterung | f,-en | extension
|
| Erweiterungsideal | | extension ideal
|
| Erweiterungsmodul | | extension module
|
| erzeugen | vt | to produce, to generate
|
| Erzeugend | | generator
|
| Erzeugendenzahl | | number of generators
|
| erzeugt | adj | generated
|
| Erzeugung | f | generation
|
| etwas | adv | a little
|
| etwas | pron | something, anything, little
|
| euklidisch | adj | Euclidean
|
| eulersche Funktion | | Euler's totient function
|
| eventuell | adj | possible
|
| eventuell | adv | possibly, perhaps
|
| exakt | adj | exact
|
| Exaktheit | f | exactness
|
| Existenz | f,-en | existence
|
| existieren | vi | to exist
|
| exzellenter Ring | | excellent ring
|
| f�hig | adj | capable, able
|
| Faktor | m,-en | factor
|
| Faktorgruppe | f,-n | factor group, quotient group
|
| faktoriell | adj | (ring) factorial
|
| Faktorisierung | f | factorization
|
| Faktorzerlegung | f | factorization
|
| Fall | m,�e | case
|
| fallen | vi | to fall, descend, decrease
|
| falls | adv | in case, if
|
| Familie | f | family
|
| Faser | f,-n | fiber
|
| Faserprodukt | | fiber product
|
| Fasersumme | | fiber sum
|
| fa� | vb | takes
|
| fassen | vt | to take, to set
|
| fast | adv | nearly, almost
|
| Fehler | m,- | error, mistake
|
| fermatsche Primzahl | | Fermat's prime
|
| ferner | adv | moreover, as well as
|
| fertig | adj | ready, finished, done
|
| fest | adj | fixed
|
| festgelegt | vb | pp of festlegen
|
| festlegen | vt | to fix
|
| Figur | f,-en | figure
|
| finden | vt | to find
|
| Fittingideal | -e | fitting ideal
|
| Fittinginvariant | -en | fitting invariant
|
| Fixk�rper | | fixed field
|
| flach | adj | flat
|
| flach Modul | | flat module
|
| Fl�che | f,-n | surface
|
| Fl�cheninhalt | m,-e | area
|
| Folge | f,-n | sequence, series
|
| folgen | vi | to follow
|
| folgend | adj | following
|
| folgenden | | im folgenden - in the following
|
| folgenderma�en | adv | as follows, in the following way
|
| Folgerung | f,-en | consequence, conclusion
|
| folglich | adv | consequently
|
| Form | f,-en | form, shape
|
| formal | adj | formal
|
| Formel | f,-n | formula
|
| Formenring | | form-ring
|
| formulieren | vt | to formulate
|
| fortfahren | vi | to continue
|
| fortschreiten | vi | to proceed, to advance, to progress
|
| fortsetzen | vt | to extend to, to continue
|
| Fortsetzung | f | continuation
|
| Frage | f,-n | question
|
| fragen | vt | to ask
|
| frei | adj | free
|
| fr�her | adv | earlier
|
| f�hren | vt | to lead, to carry
|
| F�hrer | m,- | conductor
|
| fundamental | adj | fundamental
|
| Fundamentalsatz der Algebra | | fundamental theorem of algebra
|
| Funktion | f,-en | function
|
| Funktionenk�rper | | function field
|
| Funktionskeim | | function germ
|
| f�r | prep | for
|
| Fu�punkt | | foot of perpendicular
|
| Galoiserweiterung | | Galois extension
|
| Galoisgruppe | | Galois group
|
| Galoistheorie | | Galois theory
|
| ganz | adj | integral
|
| ganz | adj | whole, complete
|
| ganz | adv | quite, completely, exactly
|
| ganze abgeschlossen | | integrally closed
|
| ganze Abschlie�ung | | integral closure
|
| ganze Zahl | | integer
|
| ganzzahlig | adj | integral
|
| Garbe | f,-n | sheaf
|
| gau�chen | adj | Gaussian, Ring der ganzen ~ Zahlen - ring of Gaussian intergers
|
| geben | vt | to give
|
| Gebiet | nt,-e | area, plane region
|
| geboten | adj | necessary, advisable
|
| Gebrauch | m,�e | use
|
| gebrauchen | vt | to employ
|
| gebrochen | adj | fractional
|
| geeignet | adj | suitable
|
| gegeben | adj | given
|
| gegeben | vb | pp of geben
|
| gegenseitig | adj | mutual, reciprocal
|
| gegenseitig | adv | mutually
|
| Gegenstand | m | subject
|
| gegen�ber | prep | under
|
| geh�ren | vi | to belong
|
| geh�rt | vb | belongs
|
| gelangen | vi | ~ an/zu - to reach, attain, get
|
| gelangt | vb | pp of langen
|
| gelten | vi | to hold, to be valid
|
| gem�� | prep | (+ dat.) in accordance with, according to
|
| gemein | adj | common
|
| gemeinsam | adj | common
|
| gemeinsam | adv | in common, together
|
| genau | adj | exact, precise
|
| genau | adv | exactly, precisely, genau dann ..., wenn ... - ... if and only if ...
|
| Genaueres | pl | further details; more precise statements
|
| Genauigkeit | f | exactness, accuracy, precision
|
| Generalisierung | f | generalization
|
| generisch | adj | generic
|
| gen�gen | vi | to be enough, to suffice
|
| gen�gt | vb | is sufficient
|
| Geometrie | f | geometry
|
| geometrisch | adj | geometric
|
| geordnet | adj | ordered
|
| gerade� | adj | even (number)
|
| gerade� | adv | just, exactly
|
| gerade� | adj | straight
|
| Gerade | f,-n | straight line
|
| gerade Permutation | | even permutation
|
| gerade Zahl | | even number
|
| Geradenb�ndel | | line bundle
|
| gering | adj | small, low, short
|
| gesamt | adj | whole, entire
|
| Gesamtheit | f | whole, totality
|
| geschehen | vi | to happen
|
| geschrieben | vb | pp of schreiben
|
| Gesetz | nt,-e | law, rule
|
| Gestalt | f,-en | form, shape
|
| gesucht | adj | desired, sought for
|
| gewinnen | vt | to gain (confidence), to obtain, to improve, to win
|
| gewi� | adj | certain
|
| gew�hnlich | adj | ordinary, usual
|
| gewohnt | adj | usual, wie ~ - as usual
|
| g.g.T. | abbr | (= gr��ter gemeinschaftlicher Teiler) gcd
|
| gibt | vb | tps of geben, es gibt - there is/are
|
| gilt | vb | holds, es ~ - we have
|
| Gitterpunkt | -e | lattice point
|
| glatt | adj | smooth, nonsingular
|
| gleichbedeutend | adj | equivalent
|
| gleiche | | das ~ - (phenomenon, thing) the similar (same)
|
| Gleichheit | f | equality
|
| Gleichheitszeichen | | equality sign
|
| Gleichung | f | equation
|
| Gleichungssystem | nt,-e | system of equations
|
| gleichzeitig | adj | simultaneous
|
| Glied | nt,-er | term
|
| gliedweise | adj,adv | term by term, termwise
|
| global | adj | global
|
| Gorensteinring | | Gorenstein ring
|
| Grad | m,-e | degree
|
| graduiert | adj | graded
|
| graduierte Ring | | graded ring
|
| Graduierung | f | grading
|
| gro� | adj | big, large, great
|
| gr��te | adj | largest
|
| gr��ter gemeinschaftlicher Teiler | | greatest common divisor
|
| Grund | m,�e | reason, auf ~ von - on the basis of
|
| Grundbegriff | | basic concept
|
| Grundeigenschaft | f | basic property
|
| Grundk�rper | | a field whose extensions are studied
|
| grundlegend | adj | fundamental
|
| Gruppe | f,-n | group
|
| Gruppenstruktur | | group structure
|
| Gruppentafel | f,-n | table of a group (operation), Cayley diagram
|
| g�ltig | adj | valid
|
| G�ltigkeit | f | validity
|
| kanonische | adj | canonical
|
| Kante | f,-n | edge
|
| Kapitel | nt,- | chapter
|
| Kardinalit�t | f | cardinality
|
| kartesische | adj | cartesian
|
| Kategorientheorie | | category theory
|
| Kegel | m,- | cone
|
| keineswegs | adv | by no means, in no way
|
| kennen | vt | to know
|
| Kenntnis | f,-se | knowledge
|
| Kennzeichnung | f | criterion, characterization
|
| Kern | m,-e | kernel
|
| Kette | f,-n | chain
|
| Kettenbruch | | continued fractions
|
| Kettenring | m,- | chain ring
|
| k-fach basisch | | (of a submodule) k-times basic
|
| k.g.V. | abbr | (= kleinstes gemeinschaftliches Vielfaches) lcm
|
| Klammer | f,-n | bracket
|
| klar | adj | clear
|
| Klasse | f,-n | class
|
| Klasse | f,-n | coset
|
| Klasseneinteilung | | classification
|
| klassengleichung | | class equation
|
| klassenzahl | | class number
|
| klassisch | adj | classical
|
| klein | adj | small
|
| kleiner | adj | smaller
|
| kleiner fermatscher Satz | | Fermat's little theorem
|
| kleinst | adj | smallest
|
| kleinstes gemeinschaftliches Vielfaches | | least common multiple
|
| Kodimension | f | codimension
|
| Koeffizient | m,-en | coefficient
|
| Koh�he | f,-n | coheight
|
| Kokern | m,-e | cokernel
|
| komaximal | adj | comaximal
|
| Kombination | f,-en | combination
|
| kombinatorisch | adj | combinatorial
|
| kombinieren | vt,vi | to combine, to deduce, to work out
|
| kommutativ | adj | commutative
|
| kommutative Gruppe | | commutative group
|
| Kommutativit�t | f | commutativity
|
| Kommutator | m,-en | commutator
|
| Kommutatorgruppe | | commutator (sub)group
|
| kommutieren | vi | to commute
|
| Komplement�rmenge | | complementary set, set difference
|
| Komplement | m,-en | complement
|
| komplettiert | adj | completed
|
| Komplettierung | f | completion
|
| komplex | adj | complex (number)
|
| komplexe Zahl | | complex number
|
| Komplexifizierung | | complexification
|
| Komplexit�t | f | complexity
|
| kompliziert | adj | complicated
|
| Komponent | m,-en | component
|
| komponentenweise | adj | componentwise
|
| komponieren | vt | to compose
|
| Komposition | f | composition
|
| Kompositionsfolge | | composition series
|
| Kompositionsreihe | | composition series
|
| Kongruenz | f,-en | congruence
|
| Konjugiert | -en | conjugate
|
| konkret | adj | concrete
|
| Konormalenmodul | | conormal module
|
| Konsequenz | f,-en | consequence, conclusion, consistency
|
| konstant | adj | constant
|
| konstruierbar | adj | constructible
|
| Konstruierbarkeit | | constructibility
|
| konstruieren | vt | to construct
|
| Konstruktion | f,-en | construction
|
| konstruktiv | adj | constructive
|
| Konvention | f | convention
|
| konvex | adj | convex
|
| Koordinat | | coordinate
|
| Koordinatenring | | coordinate ring
|
| Koordinatensystem | | coordinate system
|
| Koordinatentransformation | | coordinate transformation
|
| Korollar | m,-e | corollary
|
| K�rper | m,- | field
|
| K�rperadjunktion | | field obtained by adjoining one or more elements to a field
|
| K�rpererweiterung | | field extension
|
| k�rpertheoretisch | | field-theoretic
|
| Kreis | m,-e | circle
|
| Kreisteilungspolynom | | cyclotomic polynomial
|
| kriterium | nt | criterion
|
| Krulldimension | f | Krull dimension
|
| Kurve | f,-n | curve
|
| kurz | adj | short
|
| k�rzer | adv | in short
|
| K�rzungsregel | | cancellation law
|
| n-dimensional | adj | n-dimensional
|
| n-Eck | | n-gon, polygon with n edges, regul�r ~ - regular polygon with n edges
|
| n-fache Nullstelle | | zero of order n
|
| n-reihig | adj | n-rowed
|
| n-te | adj | nth
|
| n-te Wurzel | | nth root
|
| n-tupel | | n-tuple
|
| nach | prep | according to; by; with respect to; from
|
| Nachpr�fung | f | checking, verification
|
| Nachsilbe | f,-n | suffix
|
| Nachteil | m | disadvantage
|
| Nachweis | m,-e | proof
|
| N�he | f,- | neighborhood, in der ~ - in the neighborhood
|
| naheliegend | adj | obvious
|
| n�her | adj | closer, more detailed
|
| N�herung | f,-en | approximation, approximate value
|
| n�herungsweise | adj | approximate
|
| N�herungswert | m | approximate value
|
| n�mlich | adv | namely
|
| nat�rlich | adj | natural
|
| nat�rlich | adv | naturally
|
| nat�rliche Zahl | | natural number
|
| neben | prep | (+ dat) apart from, besides
|
| negativ | adj | negative
|
| nehmen | vt | to take
|
| nennen | vt | to name, to call
|
| Nenner | m,- | denominator
|
| Nennermenge | | denominator set
|
| Netz | nt,-e | net, network, web
|
| neutrale Element | | identity element
|
| nicht-aufl�sbar | adj | non-solvable
|
| nicht konstant | | non-constant
|
| nicht-negativ | adj | nonnegative
|
| nichttrivial | adj | nontrivial
|
| niedrig | adj | low
|
| niemals | adv | never
|
| nilpotent | adj | nilpotent
|
| Nilradikal | nt | nilradical
|
| nimmt | vb | takes
|
| noethersch | adj | Noetherian
|
| normal | adj | normal (extension)
|
| normale Untergruppe | | normal subgroup
|
| normalerweise | adv | normally
|
| Normalfolge | | normal series
|
| Normalisator | m,-en | normalizer, centralizer
|
| Normalisierung | f | normalization
|
| Normalreihe | f,-n | normal series
|
| Normalteiler | | normal subgroup
|
| normiert | adj | monic (polynomial)
|
| notieren | vt | to note
|
| n�tig | adj | necessary, wenn ~ - if necessary
|
| notwendig | adj | necessary, nicht ~ - not necessarily
|
| Notwendigkeit | f | necessity
|
| Nullelement | | zero element
|
| Nullideal | | the zero ideal
|
| Nullpolynom | | the zero polynomial
|
| Nullpunkt | | zero point
|
| Nullring | | zero ring
|
| Nullstelle | f,-n | zero (of a polynomial)
|
| Nullstellenmenge | | zero set
|
| Nullstellenordnung | | order of zero
|
| Nullteiler | m | zero divisor
|
| nullteilerfrei | adj | free of (non-zero) zero divisors
|
| Nullvektor | m,-en | zero vector
|
| numerieren | vt | to number
|
| Numerierung | f | numbering
|
| numerisch | adj | numerical
|
| numerische Integration | | numerical integration
|
| nur | adv | only, ein und ~ ein - one and only one
|
| n�tzlich | adj | useful
|
| s�mtlich | adj | all (the); complete
|
| Satz | m,�e | theorem; proposition; sentence; clause
|
| scharf | adj | sharp
|
| Schema | nt,-s or -ta | scheme
|
| Schiefk�rper | | division ring
|
| Schlangenlemma | | snake lemma
|
| schlechthin | adv | absolutely
|
| schlichtes Produkt | | internal direct product
|
| schlie�en | vt | ~ aus - to infer from
|
| Schlu� | m,�sse | end, conclusion
|
| Schl�sselrolle | f,-n | key role
|
| Schlu�weise | f | argument
|
| schneiden | vt | to cut, to intersect
|
| Schnittmultiplizit�t | | intersection multiplicity
|
| Schnittpunkt | -e | point of intersection
|
| Schnittschema | | intersection scheme
|
| schon | adv | already
|
| Schranke | f,-n | barrier, limit
|
| schreiben | vt | to write
|
| Schreibweise | f | notation, spelling
|
| Schritt | m,-e | step
|
| schwierig | adj | difficult, hard
|
| Schwierigkeit | f | difficulty
|
| sei | vb | A sei B - Let A be B
|
| seien | vb | A und B seien C - Let A and B be C.
|
| sein | vi | to be
|
| Seite | f,-n | side, (of a book) page
|
| selbst | pron | itself, himself, herself etc.
|
| selbst�ndig | adj | independent
|
| semilokal | adj | semilocal
|
| senkrecht | adj | vertical, perpendicular
|
| Senkrechte | | perpendicular
|
| Separabilit�tsgrad | | separability degree
|
| separable | adj | separable
|
| separable H�lle | | separable closure
|
| setzen | vt | to set, to put, to place
|
| sicher | adv | certainly
|
| sicherstellen | vt | to guarantee
|
| simulieren | vt | to simulate
|
| singul�rer Punkt | | singular point
|
| Singularit�t | f | singularity
|
| singularit�tenfrei | | nonsingular
|
| Sinn | m,-e | sense, im Sinne - in the sense (that), im welchem Sinne - in what sense
|
| sinnvoll | adj | meaningful, sensible
|
| Situation | f | situation
|
| Skalarmultiplikation | | scalar multiplication
|
| Skizze | f,-n | sketch
|
| skizzieren | vt | to sketch
|
| so da� | | such that
|
| Sockel | m,- | socle
|
| sofort | adv | immediately, at once
|
| Software | f,-s | software
|
| Softwaretechnologie | | software technology
|
| sog. | abbr | (= sogenannt) so-called
|
| sogar | adv | even, also
|
| solch | adj | such
|
| sowohl | conj | ~ ... als/wie auch ... - both ... and ...
|
| Spalte | f,-n | column
|
| sparen | vt,vi | to save
|
| sp�ter | adv | later
|
| Speicher | m,- | (computer) memory
|
| speichern | vt | (computer) to store
|
| Spektrum | nt,Spektren | spectrum
|
| spezialisieren | vi | to specialize
|
| Spezialisierung | f | specialization
|
| Spezialit�t | f | speciality
|
| speziell | adj | special
|
| Spezifikation | f | specification
|
| spezifisch | adj | specific
|
| Sph�re | f,-n | sphere
|
| spielen | vt | to play (a role etc.)
|
| Spitze | f,-n | vertex
|
| Spur | f,-en | trace
|
| stammen | vi | ~ von/aus - to come from, to be due to
|
| station�r | adj | stationary
|
| statt | prep | (+ gen. or acc.) instead of
|
| steigen | vi | to rise, increase, ascend
|
| Stelle | f,-n | place
|
| stetig | adj | continuous
|
| Stetigkeit | f | continuity
|
| stets | adv | always
|
| Stillstand | m | standstill
|
| strahl | m,-en | ray, beam
|
| Strategie | f | strategy
|
| Strecke | f,-n | line
|
| Struktur | f | structure
|
| Strukturgarbe | | structure sheaf
|
| Studium | nt,pl | studies
|
| Substitution | f | substitution
|
| subtrahieren | vt | to subtract
|
| Subtraktion | f | subtraction
|
| Summe | f,-n | sum, total
|
| summieren | vt | to add up
|
| Supremum | nt | supremum
|
| surjektiv | adj | surjective
|
| Surjektivit�t | f | surjectivity
|
| Sylowgruppe | | Sylow group
|
| Sylow-Untergruppe | | Sylow subgroup
|
| symbolisch | adj | symbolic
|
| symmetrisch | adj | symmetric
|
| System | nt,-e | system
|
| systematisch | adj | systematic
|
| Syzygienmodul | | syzygy module
|
| �ben | vt,vi | to practice, to exercise
|
| �ber | prep | about
|
| �berabz�hlbar | adj | uncountable, non-denumerable
|
| �beraus | adv | exceedingly
|
| �berblick | m | survey, overview
|
| �berdecken | vt | to cover
|
| �berdeckung | f | cover
|
| �berdies | adv | besides, moreover
|
| �bereinstimmen | vi | to agree, to tally, to coincide
|
| �bereinstimmung | f | agreement
|
| �berfl�ssig | adj | superfluous, redundant
|
| �bergang | m | passage, transition, crossing
|
| �bergehen | vi | to reduce to
|
| �berlegen | vt | to consider
|
| �berlegung | f,-en | consideration
|
| �berpr�fen | vt | to examine, to check
|
| �berschu� | m | surplus, excess
|
| �bertragen | vt | to transfer, to apply
|
| �berwiegend | adj | predominant
|
| �berwiegend | adv | predominantly
|
| �berzeugen | vt | to convince
|
| �berzeugt | vb | man �berzeugt - it is easily seen
|
| �blich | adj | usual
|
| �brig | adj | remaining, other
|
| um zu | | in order to
|
| umfassen | vt | to include, to contain
|
| umfassend | adj | containing
|
| umfa�t | vb | tps of umfassen
|
| Umformung | f,-en | transformation
|
| Umgebung | f | neighborhood
|
| umgehen | vi | mit jdm/etw ~ k�nnen - to know how to handle sb/sth
|
| umgekehrt | adv | inversely, wenn ~ - conversely
|
| Umkehrabbildung | f | inverse map
|
| umkehren | vt | to reverse
|
| umkehrend | adj | reversing
|
| umst�ndlich | adj | complicated
|
| unabh�ngig | adj | ~ von - independent of
|
| Unbestimmte | | indeterminate
|
| unendlich | adj | infinite
|
| unendlich | adv | infinitely
|
| unendlich | adj | infinity
|
| unendlich ferne Hyperebene | | hyperplane at infinity
|
| unendlich ferne Punkt | | point at infinity
|
| ungef�hr | adj | rough, approximate
|
| ungef�hr | adv | roughly, approximately
|
| ungemischt | adj | unmixed
|
| Ungemischtheit | f | unmixedness
|
| ungerade | adj | odd, uneven
|
| ungerade Permutation | | odd permutation
|
| ungew�hnlich | adj | unusual
|
| Ungleichung | f | inequality
|
| unimodular | adj | unimodular
|
| universal-K�rper | | universal field
|
| universell | adj | universal
|
| unmittelbar | adj | immediate, direct
|
| unmittelbar | adv | immediately, directly
|
| unn�tig | adj | unnecessary
|
| unschwer | adj | easily, without difficulty
|
| Unterdeterminant | m,-en | subdeterminant
|
| Untergruppe | f,-n | subgroup
|
| unterliegend | adj | underlying
|
| Untermodul | nt | submodule
|
| Unterring | m,-e | subring
|
| unterscheiden | vr | to differ
|
| Unterschema | nt,-s or -ta | subscheme
|
| unterschiedlich | adj | varying, differing, different
|
| untersuchen | vt | to investigate, to examine
|
| Untersuchung | f | investigation, examination, inquiry
|
| Untervariet�t | f | subvariety
|
| Untervektorraum | | subspace (of a vector space)
|
| unverk�rzbar | adj | unshortenable, minimal
|
| unwesentlich | adj | inessential, unimportant
|
| unzerlegbar | adj | irreducible, non-decomposable
|
| Urbild | nt,-er | inverse image
|
| Ursprung | m | origin
|
| Variable | f,-n | variable
|
| Variablentauschtrick | | variable exchange trick
|
| Variblenzahl | f | number of variables
|
| Variet�t | f,-en | variety
|
| Vektor | m,-en | vector
|
| Vektorraumb�ndel | nt,- | vector bundle
|
| verallgemeinern | vt | to generalize
|
| verallgemeinert | adj | generalized
|
| Verallgemeinerung | f | generalization
|
| Ver�nderlich | | variable
|
| Verbesserung | f | improvement, correction
|
| verbinden | vt | to connect, to combine
|
| Verbindung | f | connection, combination
|
| verbleiben | vi | to remain
|
| Vereinfachung | f | simplification, reduction
|
| vereinfachen | vt | to simplify, reduce
|
| Vereinigung | f | union
|
| Verf�gung | f | zur ~ - at one's disposal
|
| Verfahren | nt,- | process, procedure
|
| Verfeinerung | f | refinement
|
| Vergleich | m,-e | comparison, im ~ zu - in comparison with
|
| vergleichen | vt | to compare
|
| vergr��ern | vt | to increase, enlarge, magnify
|
| verhalten | vb | to be in proportion to
|
| Verh�ltnis | nt,-se | proportion, ratio
|
| verifizieren | vt | to verify
|
| verkleben | vt | to glue up, stick, combine
|
| verkleinern | vt | to decrease, to reduce
|
| Verkn�pfung | f,-en | operation, operator
|
| Verkn�pfungstafel | | table of operation, Cayley diagram
|
| verk�rzen | vt | to shorten
|
| Verk�rzung | f | shortening
|
| verl�ngern | vt | to extend, to lengthen
|
| verl�ngert | adj | lengthened
|
| Verlauf | m | locus
|
| verlaufen | vi | to proceed
|
| Verletzung | f | violation
|
| vermeiden | vt | to avoid
|
| vermitteln | vt | to arrange, to find
|
| Vermutung | f | conjecture
|
| versch�rfen | vt | to sharpen, to intensify
|
| verschieden | adj | different, von Null ~ - nonzero
|
| verschwinden | vi | to vanish
|
| verschwindend | adj | vanishing
|
| Verschwindungsideal | | vanishing ideal
|
| versehen | vt | to provide
|
| verstanden | vb | pp of verstehen
|
| verstehen | vt | to understand
|
| Versuch | m,-e | attempt, experiment
|
| versuchen | vt | to try, to attempt
|
| vertauschen | vt | to exchange
|
| verteilen | vt | to distribute, to assign
|
| vertr�glich | adj | commuting
|
| Vertrauen | nt,-s | confidence
|
| verwenden | vt | to use, to apply
|
| Verwendung | f | use, application
|
| verzichten | vi | ~ auf - to forego, to give up, to avoid
|
| vgl. | abbr | (= vergleiche) cf.
|
| viel | adj | many
|
| Vielfache(s) | nt | multiple
|
| Vielfachheit | f | multiplicity
|
| voll | adj | full
|
| voll | adv | fully
|
| voller Quotientenring | | full ring of fractions
|
| v�llig | adj | complete
|
| v�llig | adv | completely
|
| vollkommen | adj | perfect (field)
|
| vollst�ndig | adj | complete, total
|
| vollst�ndig | adv | completely, totally
|
| vollst�ndig geordnet | | totally (or lineraly) ordered (set)
|
| Volumen | nt,- or Volumina | volume
|
| voraussetzen | vt | to assume
|
| Voraussetzung | f | assumption, hypothesis
|
| vorgehen | vi | to go ahead, to proceed
|
| vorhanden | adj | existing, available
|
| vorherig | adj | previous
|
| vorkommen | vi | to come forward, to occur, to appear
|
| vorliegend | adj | present, current
|
| vorschreiben | vt | to specify
|
| Vorsicht | f | care, caution
|
| vorsichtig | adj | careful
|
| Vorsilbe | f,-n | prefix
|
| vorstellen | vt | to put in front, to introduce, to represent
|
| Vorteil | m,-e | advantage, ~ gegen�ber - advantage over
|
| vorteilhaft | adj | advantageous
|
| Vorzeichen | nt | sign
|
| wachsen | vi | to grow
|
| Wahl | | choice
|
| w�hlen | vt | to choose
|
| w�hrend | prep | during
|
| wahrscheinlich | adj | probable, likely
|
| Wahrscheinlichkeit | f | probability, likelihood, chance
|
| Wahrscheinlichkeitsdichte | f | probability density
|
| Wahrscheinlichkeitsfunktion | f | probability function
|
| Wahrscheinlichkeitsverteilung | f | probability distribution
|
| Warnung | f | warning
|
| weder | conj | neither; ~ ... noch ... - neither ... nor ...
|
| Weg | m | path, way, track
|
| weglassen | vt | to leave out, to omit
|
| weierstra�cher Nullstellensatz | | Weierstrass' zero theorem
|
| weil | conj | because
|
| Weise | f,-n | manner, way
|
| weiter | adj,adv | further
|
| weiterhin | conj | furthermore
|
| Weiterung | f | extension
|
| wenig | adj,adv | little, ein ~ - a little
|
| wenige | pl | few
|
| wenigstens | adv | at least
|
| Werkzeug | nt,-e | tool
|
| Wert | m,-e | value
|
| wesentlich | adj | significant, considerable, essential
|
| weshalb | adv | why, on account of which
|
| wichtig | adj | important
|
| widersprechen | vi | to contradict
|
| widersprechend | adj | contradictory
|
| Widerspruch | m | contradiction
|
| wie | prep | as
|
| wie oben | | as above
|
| wiederholen | vt | to repeat
|
| wiederholt | adj | repeated
|
| Wiederholung | f | repetition
|
| wiederum | adv | again, in turn, on the other hand
|
| willk�rlich | adj | arbitrary
|
| Winkel | m,- | angle
|
| Winkelhalbierung | | bisection of angle
|
| wirklich | adj | real, actual
|
| wirklich | adv | really, actually
|
| Wirklichkeit | f | reality
|
| Wirkungsbereich | m | support
|
| wobei | conj | where
|
| wohl | adv | probably, perhaps
|
| wohldefiniert | adj | well-defined
|
| W�rfel | m,- | cube, dice
|
| Wurzel | f,-n | root, square root
|