Commutative binary operation
This article defines a property of binary operations (and hence, of magmas)
This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Definition with symbols
Let be a set and be a binary operation on (viz, is a map × → . Then, is said to be commutative if, for every in , the following identity holds:
If the above equation holds for particular values of and , we say that and commute.
A magma where the binary operation is commutative is termed a commutative magma. For a semigroup, monoid or group, we use the word Abelian as an alternative to commutative (thus, a group where the binary operation is commutative is termed an Abelian group).