commutative

English

Adjective

commutative (not comparable)

1. (mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.

   Addition on the real numbers is commutative because for any real numbers $s,t$, it is true that $s+t=t+s$.

2. (algebra, of an algebraic structure) Having a commutative operation.
3. (mathematics, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.

Synonyms

• (of an algebraic structure): abelian, Abelian

Translations

mathematics: such that order of operands does not affect result

• Czech: komutativní (cs) m
• Dutch: commutatief (nl)
• Finnish: kommutatiivinen (fi), vaihdannainen (fi)
• German: kommutativ (de)

• Greek: αντιμεταθετικός (el) (antimetathetikós)
• Icelandic: víxlinn (is) m
• Polish: przemienny (pl) m
• Portuguese: comutativo (pt) m, comutativa (pt) f

algebra: having a commutative operation

• Czech: komutativní (cs) m
• Finnish: kommutatiivinen (fi), vaihdannainen (fi)

• German: kommutativ (de)
• Portuguese: comutativo (pt) m, comutativa (pt) f

The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Help:How to check translations.

Translations to be checked

• Catalan: commutatiu m, commutativa f (1, 2), abelià m, abeliana f (2)
• French: commutatif m, commutative f (1, 2), abélien m, abélienne f (2)

• Hungarian: kommutatív
• Spanish: conmutativo (1, 2)

Related terms

• anticommutative
• commutator
• commute
• commutative justice
• commutative ring

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French

Adjective

commutative

1. feminine form of commutatif

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Italian

Adjective

commutative f

1. feminine plural of commutativo