# Commutative binary operation

*This article defines a property of binary operations (and hence, of magmas)*

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## Definition

### 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**.

### Related term

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).

## Related element properties

### Central element

`Further information: central element`
An element in a magma is termed central if it commutes with every element. The set of central elements of a magma is termed the commutative center.