different between anticommutative vs commutative

English

Etymology

anti- +? commutative

Adjective

anticommutative (not comparable)

1. (algebra) Of an operator * for which a * b = - (b * a)

Related terms

• commutative

Translations

English

Etymology

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

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 ${\displaystyle s,t}$, it is true that ${\displaystyle s+t=t+s}$.

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

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

Related terms

Translations

References

• commutative property on Wikipedia.Wikipedia

French

Adjective

commutative

1. feminine singular of commutatif

Italian

Adjective

commutative

1. feminine plural of commutativo