different between associative vs commutative

English

Etymology

From associate +? -ive.

Pronunciation

• (US) IPA^(key): /??so?.?i.?.t?v/, /??so?.si.?.t?v/

Adjective

associative (comparative more associative, superlative most associative)

1. Pertaining to, resulting from, or characterised by association; capable of associating; tending to associate or unite.
   • 1998, Kazimierz Zieli?ski, Pairing, Continuity, Contingency - What's the Difference, Anna Neugebauer (editor), Macromolecular Interplay in Brain Associative Mechanisms: Proceedings of the International School of Biocybernetics, World Scientific, page 63,

     At present conditioning is viewed as a special case of associative learning which provides an animal (and human being alike) with die ability to discover, memorize, retrieve, and use relationships between signals and reinforcers and also to control rewards and aversive events.

2. (algebra, of a binary operator ${\displaystyle *}$) Such that, for any operands ${\displaystyle a,b}$ and ${\displaystyle c}$, ${\displaystyle (a*b)*c=a*(b*c)}$; (of a ring, etc.) whose multiplication operation is associative.
   • 2000, Freddy Van Oystaeyen, Algebraic Geometry for Associative Algebras, Marcel Dekker, page 235,

     Perhaps it is an advantage of the "associative algebraic geometry" we have tried to develop in foregoing chapters that it is independent of braidings and further generalizations because it will remain valid as long as the corresponding "function"-rings constructed in these theories are associative algebras.

   • 2006, Ibrahim Assem, Daniel Simson, Andrzej Skowro?ski, Elements of the Representation Theory of Associative Algebras, 1: Techniques of Representation Theory, Cambridge University Press, page vii,

     It is now generally accepted that the representation theory of associative algebras traces its origin to Hamilton's description of the complex numbers by pairs of real numbers.

   • 2014, Miguel Cabrera García, Ángel Rodríguez Palacios, Non-Associative Normed Algebras, Volume 1: The Vidav–Palmer and Gelfand-Naimark Theorems, Cambridge University Press, page 1,

     In this section we develop the basic theory of normed algebras, putting special emphasis on the case of complete normed unital associative complex algebras.

3. (computing) Addressable by a key more complex than an integer index.

Antonyms

• antiassociative

Hyponyms

Derived terms

Related terms

• associative array

Translations

Danish

Adjective

associative

1. neuter singular of associativ

French

Pronunciation

• IPA^(key): /a.s?.sja.tiv/

Adjective

associative

1. feminine singular of associatif

Italian

Adjective

associative f pl

1. feminine plural of associativo

Anagrams

• associatevi

Swedish

Adjective

associative

1. absolute definite natural masculine form of associativ.

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