Language/Multiple-languages/Vocabulary/Algebra

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eng-Latn-US: concept	cmn-Hans-CN: 概念	cmn-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]	fra-Latn-FR: concept [m]	jpn-Jpan-JP: 概念	jpn-Hrkt-JP: が↓いねん	rus-Cyrl-RU: конце́пция

algebra	代数	dàishù	Algebra [f]	algèbre [f]	代数学	だ↑いす↓うがく	а́лгебра
elementary algebra	初等代数	chūděng dàishù	elementare Algebra	algèbre [f] élémentaire, algèbre [f] classique	初等代数学	しょ↑とうだいす↓うがく	элемента́рная а́лгебра
abstract algebra	抽象代数	chōuxiàng dàishù	abstrakte Algebra	algèbre [f] générale, algèbre [f] abstraite	抽象代数学	ちゅ↑うしょうだいす↓うがく	общая а́лгебра, абстра́ктная а́лгебра, вы́сшая а́лгебра
group theory	群论	qún lùn	Gruppentheorie [f]	théorie [f] des groupes	群論	ぐ↓んろん	тео́рия групп
ring theory	环论	huán lùn	Ringtheorie [f]	théorie [f] des anneaux	環論	か↑んろん	тео́рия коле́ц
category theory	范畴论	fànchóu lùn	Kategorientheorie [f]	théorie [f] des catégories	圏論	け↑んろん	тео́рия катего́рий
commutative algebra	交换代数	jiāohuàn dàishù	kommutative Algebra	algèbre [f] commutative	可換環論	か↑かんか↓んろん	коммутати́вная а́лгебра
linear algebra	线性代数	xiànxìng dàishù	lineare Algebra, Vektoralgebra [f]	algèbre [f] linéaire	線型代数	せ↑んけいだいす↓うがく	лине́йная а́лгебра
multilinear algebra	多重线性代数	duōchóng xiànxìng dàishù	multilineare Algebra	algèbre [f] multilinéaire	多重線型代数	た↑じゅうせんけいだいす↓う	полилине́йная а́лгебра
universal algebra, common algebra	泛代数	fàn dàishù	universelle Algebra, allgemeine Algebra	algèbre [f] universelle	普遍代数学，一般代数学	ふ↑へんだいすう↓がく，い↑っぱんだいすう↓がく	универса́льная а́лгебра
homological algebra	同调代数	tóngdiào dàishù	homologische Algebra	algèbre [f] homologique	ホモロジー代数学	ホ↑モロジ↓ーだいす↑うがく	гомологи́ческая а́лгебра

Basics of Algebra

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]	fra-Latn-FR: concept [m]

algebraic equation	coefficient
algebraic expression	expression <mathematical logic>; integer; constant; variable; algebraic operation
algebraic fraction	fraction; algebraic expression
algebraic operation	operation <mathematical logic>
algebraic fraction	fraction; algebraic expression
coefficient	multiplication <number theory>; expression <mathematical logic>
constant function	constant <number theory>; function
dependent variable	fraction; operand <mathematical logic>	因变量	yīn biànliàng	abhängige Variable
equation	equality <mathematical logic>; expression <mathematical logic>	方程，等式	fāngchéng, děng shì	Gleichung [f]	équation [f]
even function	function <mathematical logic>; line symmetry <geometry>
identity	equality <mathematical logic>
identity element, neutral element	set <mathematical logic>; binary operation <mathematical logic>
independent variable, argument of a function	function <mathematical logic>	自变量	zì biànliàng	unabhängige Variable
indeterminate	variable
inequation	inequality <mathematical logic>	不等式	bùděng shì	Ungleichung [f]	inéquation [f]
irreducible polynomial	polynomial; factorization
linear equation	equation; coefficient
left identity	identity element <mathematical logic>
odd function	function <mathematical logic>; point symmetry <geometry>
partial fraction decomposition, partial fraction expansion	algebraic fraction; polynomial
polynomial	expression <mathematical logic>; coefficient; indeterminate
quadratic equation	equation; coefficient
rational function	algebraic fraction; polynomial
right identity	identity element <mathematical logic>
solution	equation
square	exponentiation <number theory>
system of equations, simultaneous equations	finite set <mathematical logic>; equation
variable	mathematical object <mathematical logic>
unknown	variable
zero; root	domain; solution

Abstract Algebra

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Jpan-JP: 概念	jpn-Jpan-JP: 前提	jpn-Hrkt-JP: が↓いねん	jpn-Hrkt-JP: ぜ↑んてい	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка

algebraic structure	underlying set; arity; identity
arity	argument <mathematical logic>; operand <mathematical logic>
direct product	Cartesian product <mathematical logic>
field	set <mathematical logic>; basic operations <number theory>; rational number <number theory>
inverse element	set <mathematical logic>; additive inverse <number theory>; multiplicative inverse <number theory>
underlying set, carrier set	empty set <mathematical logic>

Group Theory

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Jpan-JP: 概念	jpn-Jpan-JP: 前提	jpn-Hrkt-JP: が↓いねん	jpn-Hrkt-JP: ぜ↑んてい	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка

Cayley table	finite group
group	set <mathematical logic>
finite group	underlying set; finite set <mathematical logic>
normal subgroup, invariant subgroup	subgroup; conjugation
open interval	interval
semigroup	algebraic structure; associative property
subgroup	group; binary operation <mathematical logic>

Ring Theory

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Jpan-JP: 概念	jpn-Jpan-JP: 前提	jpn-Hrkt-JP: が↓いねん	jpn-Hrkt-JP: ぜ↑んてい	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка

ring

Commutative Algebra

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Jpan-JP: 概念	jpn-Jpan-JP: 前提	jpn-Hrkt-JP: が↓いねん	jpn-Hrkt-JP: ぜ↑んてい	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка

Linear Algebra

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Jpan-JP: 概念	jpn-Jpan-JP: 前提	jpn-Hrkt-JP: が↓いねん	jpn-Hrkt-JP: ぜ↑んてい	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка

basis	linear combination
characteristic equation	characteristic polynomial
characteristic polynomial	square matrix; eigenvalue; matrix similarity; zero
conjugate matrix, Hermitian matrix	conjugate transpose
conjugate transpose, Hermitian transpose	complex conjugate <mathematical logic>; transpose
diagonal matrix	matrix; main diagonal
identity matrix	square matrix; main diagonal
invertible matrix, nonsingular matrix	identity matrix
linear combination	expression <mathematical logic>; coefficient; vector space
linear dependence	linear combination
linear independence	linear combination
linear mapping	vector addition; scalar multiplication
linear transformation	linear mapping
lower triangular matrix	triangular matrix
main diagonal	matrix; diagonal <geometry>
matrix	rectangle <geometry>; expression <mathematical logic>
matrix addition	matrix; addition <number theory>
matrix of ones	matrix
matrix multiplication	matrix; multiplication <number theory>; addition <number theory>
matrix similarity	invertible matrix
rotation matrix	linear transformation; rotation <geometry>
skew-Hermitian matrix, anti-Hermitian matrix	Hermitian matrix
square matrix	matrix; square <geometry>
system of linear equations; linear system	linear equation
transformation matrix	linear transformation; matrix
translation matrix	translation <geometry>; matrix
transpose	reflection <geometry>; main diagonal
triangular matrix	square matrix; triangle <geometry>
upper triangular matrix	triangular matrix