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

抽象代数	chōuxiàng dàishù	abstrakte Algebra	abstract algebra	algèbre générale, algèbre abstraite	抽象代数学	ちゅ↑うしょうだいす↓うがく	абстра́ктная а́лгебра, общая 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

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

代数方程	dàishù fāngchéng	algebraische Gleichung	algebraic equation	coefficient	équation polynomiale, équation [f] algébrique	代数方程式	だ↑いす↓うほ↑うて↓いしき	алгебраи́ческое уравне́ние
代数式	dàishù shì	algebraischer Ausdruck	algebraic expression	expression <mathematical logic>; integer; constant; variable; algebraic operation	expression [f] algébrique	代数式	だ↑いす↓うしき	алгебраи́ческим выраже́нием
代数分式	dàishù fēnshì		algebraic fraction	fraction; algebraic expression
			algebraic operation	operation <mathematical logic>
最大值自变量点集	zuìdàzhí zìbiànliàng diǎn jí	Argument [n] des Maximums [n]	argument of the maximum	domain <mathematical logic>; maximum <mathematical analysis>	argument [m] du maximum [m]	最大点作用素集合	さ↑いだいてんさ↓ようそしゅうごう	аргуме́нт максимиза́ции
最小值自变量点集	zuìxiǎozhí zìbiànliàng diǎn jí	Argument [n] des Minimums [n]	argument of the minimum	domain <mathematical logic>; minimum <mathematical analysis>	argument [m] du minimum [m]	最小点作用素集合	さ↑いしょうてんさ↓ようそしゅうごう	аргуме́нт минимиза́ции
二项式	èrxiàng shì	Binom [n]	binomial		binôme [m]	二項式	に↑こうしき	бино́м, двучле́н
系数	xì shù	Koeffizient [n], Beizahl [f], Vorzahl [f]	coefficient	multiplication <number theory>; expression <mathematical logic>	coefficient [f]	係数	け↑いす↓う	коэффицие́нт
常数函数	chángshù hánshù	konstante Funktion	constant function	constant <number theory>; function	fonction constante	定数関数	て↑いすうか↓んすう	конста́нтная фу́нкция, постоя́нная фу́нкция
			constant term	term <logic>; algebraic expression; constant
因变量	yīn biànliàng	abhängige Variable	dependent variable	fraction; operand <mathematical logic>	variable dépendante	従属変数	じ↑ゅうぞくへ↓んすう	зави́симая переме́нная
等式，方程	děng shì, fāngchéng	Gleichung [f]	equation	equality <mathematical logic>; expression <mathematical logic>	équation [f]
偶函数	ǒu hánshù	gerade Funktion	even function	function <mathematical logic>; line symmetry <geometry>	fonction paire	偶関数	ぐ↑うかんす↓う	чётная фу́нкция
			identity	equality <mathematical logic>
单位元，中立元	dānwèi yuán, zhōnglì yuán	neutrales Element	identity element, neutral element	set <mathematical logic>; binary operation <mathematical logic>	élément [m] neutre, élément [m] identité	単位元，中立元	た↑んいげん，ちゅ↑うりつげん	нейтра́льный элеме́нт
自变量	zì biànliàng	unabhängige Variable	independent variable	function <mathematical logic>	variable indépendante	独立変数	ど↑くりつへ↓んすう	незави́симая переме́нная
未定元	wèidìng yuán	Unbestimmte [f]	indeterminate	variable	indéterminée [f]	不定元	ふ↑ていげん	неопределённый
不等式	bùděng shì	Ungleichung [f]	inequation	inequality <mathematical logic>	inéquation [f]	不等式	ふ↑と↓うしき	неуравне́ние
代数分式	dàishù fēnshì		irrational fraction	algebraic fraction; polynomial; exponent
不可约多项式	bùkěyuē duōxiàngshì	irreduzibles Polynom	irreducible polynomial	polynomial; factorization	polynôme [m] irréductible	既約多項式	き↑やくたこ↓うしき	неприводимый многочле́н
一次方程	yīcì fāngchéng	lineare Gleichung	linear equation	equation; coefficient	équation linéaire	一次方程式	い↑ち↓じほ↑うて↓いしき	лине́йное уравне́ние
			left identity	identity element <mathematical logic>
			monomial	variable; natural number
奇函数	jī hánshù	ungerade Funktion	odd function	function <mathematical logic>; point symmetry <geometry>	fonction impaire	奇関数	き↑か↓んすう	нечётная фу́нкция
			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
可约多项式	kěyuē duōxiàngshì	reduzibles Polynom	reducible polynomial	polynomial; factorization	polynôme [m] réductible	可約多項式	か↑やくたこ↓うしき	приводимый многочле́н
			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