Language/Multiple-languages/Vocabulary/Algebra

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cmn-Hans-CN: 科目	cmn-Latn.Pinyin-CN: kēmù	deu-Latn-DE: Fach [n]	eng-Latn-US: subject	fra-Latn-FR: matière [f]	jpn-Jpan-JP: 科目	jpn-Hrkt-JP: か↑もく	rus-Cyrl-RU: предме́т
初等代数	chūděng dàishù	elementare Algebra	elementary algebra	algèbre [f] élémentaire, algèbre [f] classique	初等代数学	しょ↑とうだいす↓うがく	элемента́рная а́лгебра
抽象代数	chōuxiàng dàishù	abstrakte Algebra	abstract 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
群论	qún lùn	Gruppentheorie [f]	group theory	théorie [f] des groupes [m pl]	群論	ぐ↓んろん	тео́рия групп
环论	huán lùn	Ringtheorie [f]	ring theory	théorie [f] des anneaux [m pl]	環論	か↑んろん	тео́рия коле́ц
范畴论	fànchóu lùn	Kategorientheorie [f]	category theory	théorie [f] des catégories [f pl]	圏論	け↑んろん	тео́рия катего́рий
交换代数	jiāohuàn dàishù	kommutative Algebra	commutative algebra	algèbre [f] commutative	可換環論	か↑かんか↓んろん	коммутати́вная а́лгебра
线性代数	xiànxìng dàishù	lineare Algebra, Vektoralgebra [f]	linear algebra	algèbre [f] linéaire	線型代数	せ↑んけいだいす↓うがく	лине́йная а́лгебра
多重线性代数	duōchóng xiànxìng dàishù	multilineare Algebra	multilinear algebra	algèbre [f] multilinéaire	多重線型代数	た↑じゅうせんけいだいす↓う	полилине́йная а́лгебра
泛代数	fàn dàishù	universelle Algebra, allgemeine Algebra	universal algebra, common 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
同调代数	tóngdiào dàishù	homologische Algebra	homological 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

Main

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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 equation	coefficient
						algebraic expression	expression <mathematical logic>; integer; constant; variable; algebraic operation
						algebraic fraction	fraction; algebraic expression
						algebraic operation	operation <mathematical logic>
						argument of the maximum	domain <mathematical logic>; maximum <mathematical analysis>
						argument of the minimum	domain <mathematical logic>; minimum <mathematical analysis>
						coefficient	multiplication <number theory>; expression <mathematical logic>
						constant function	constant <number theory>; function
因变量		yīn biànliàng		abhängige Variable		dependent variable	fraction; operand <mathematical logic>
等式，方程		děng shì, fāngchéng		Gleichung [f]		equation	equality <mathematical logic>; expression <mathematical logic>	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>
自变量		zì biànliàng		unabhängige Variable		independent variable, argument of a function	function <mathematical logic>
						indeterminate	variable
不等式		bùděng shì		Ungleichung [f]		inequation	inequality <mathematical logic>	inéquation [f]
						integral expression	algebraic fraction
						irrational expression
						irrational fraction	algebraic fraction; polynomial; exponent
						irreducible polynomial	polynomial; factorization
						linear equation	equation; coefficient
						left identity	identity element <mathematical logic>
						monomial	variable; natural number
						odd function	function <mathematical logic>; point symmetry <geometry>
						parameter
						partial fraction decomposition, partial fraction expansion	algebraic fraction; polynomial
						polynomial	expression <mathematical logic>; coefficient; indeterminate
						polynomial function	polynomial; function <mathematical logic>
						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
						unknown	variable
						variable	mathematical object <mathematical logic>
						zero; root	domain; solution

Abstract Algebra

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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>
						Boolean domain	set; tautology <logic>; falsity <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

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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
						binary matrix, logical matrix, relation matrix, Boolean matrix	matrix; Boolean domain
						like terms	term <mathematical logic>
						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
						proportional function	proportionality <number theory>; function <mathematical logic>
						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

theorem in linear algebra

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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
						theorem in linear algebra
						Cayley–Hamilton theorem	characteristic polynomial; identity matrix; determinant; scalar; ring

Multilinear Algebra

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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

Universal Algebra

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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

Homological Algebra

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]	eng-Latn-US: concept	eng-Latn-US: prerequisite	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

Appendix

Sentence

cmn-Hans-CN: 语句	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: yǔjù	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Satz [m]	deu-Latn-DE: Voraussetzung [f]	eng-Latn-US: sentence	eng-Latn-US: prerequisite	fra-Latn-FR: phrase [f]	fra-Latn-FR: préalable [m]	jpn-Jpan-JP: 文章	jpn-Jpan-JP: 前提	jpn-Hrkt-JP: ぶ​↑んしょ↓う	jpn-Hrkt-JP: ぜ↑んてい	rus-Cyrl-RU: фра́за	rus-Cyrl-RU: предпосы́лка

Symbol

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

Process

cmn-Hans-CN: 过程	cmn-Hans-CN: 构件	cmn-Latn.Pinyin-CN: guòchéng	cmn-Latn.Pinyin-CN: gòujiàn	deu-Latn-DE: Prozess [m]	deu-Latn-DE: Bestandteil [m]	eng-Latn-US: process	eng-Latn-US: constituent	fra-Latn-FR: procès [m]	fra-Latn-FR: composant [m]	jpn-Jpan-JP: 過程	jpn-Jpan-JP: 構材	jpn-Hrkt-JP: か↑てい	jpn-Hrkt-JP: こ↑うざい	rus-Cyrl-RU: проце́сс	rus-Cyrl-RU: соста́вная часть

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