commutative

English

Etymology

From French commuter (“to substitute or switch”) + -ative (“tending to”). See commute.

Pronunciation

• Audio (US):

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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 $s+t=t+s$.

   Addition and multiplication are commutative operations but subtraction and division are not.

   • 2022 August 4, William Bahn, “Boolean Algebra Laws—Delving Into Boolean Identities”, in All About Circuits‎^[1]:

     The associativity of OR and AND is not at all obvious. It is tempting to assume that because OR and AND are commutative that they must be associative also. This is not the case, however, and some commutative Boolean operators are not associative. Examples include NAND and NOR.

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.
4. Relating to exchange; interchangeable.

Synonyms

• (of an algebraic structure): abelian, Abelian

Antonyms

• anticommutative

Derived terms

• cocommutative
• combinatorial commutative algebra
• commutative algebra
• commutative group
• commutative justice
• commutatively
• commutativeness
• commutative property
• commutative ring
• commutativity
• gyrocommutative
• noncommutative
• supercommutative
• uncommutative

Related terms

• commutator
• commute

Translations

mathematics: such that order of operands does not affect result

• Catalan: commutatiu (ca)
• Czech: komutativní
• Danish: kommutativ
• Dutch: commutatief (nl)
• Esperanto: komuta
• Finnish: kommutatiivinen (fi), vaihdannainen
• French: commutatif (fr)
• German: kommutativ (de)
• Greek: αντιμεταθετικός (el) (antimetathetikós)
• Hindi: विनिमेय (vinimey)
• Icelandic: víxlinn
• Indonesian: komutatif
• Polish: przemienny (pl)
• Portuguese: comutativo (pt)
• Romanian: comutativ (ro)
• Russian: коммутативный (ru) (kommutativnyj), перестановочный (ru) (perestanovočnyj)
• Tagalog: palitin
• Turkish: değişmeli (tr)

algebra: having a commutative operation

• Catalan: commutatiu (ca)
• Czech: komutativní
• Esperanto: komuta
• Finnish: kommutatiivinen (fi), vaihdannainen
• German: kommutativ (de)
• Indonesian: komutatif
• Portuguese: comutativo (pt)
• Romanian: comutativ (ro)
• Tagalog: palitin
• Turkish: değişmeli (tr)

The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.

Translations to be checked

• French: ^{(please verify)} commutatif (fr) (1, 2), ^{(please verify)} abélien (fr) (2)
• Hungarian: ^{(please verify)} kommutatív (hu)
• Spanish: ^{(please verify)} conmutativo (1, 2)

References

• commutative property on Wikipedia.Wikipedia

French

Adjective

commutative

1. feminine singular of commutatif

Italian

Adjective

commutative

1. feminine plural of commutativo