Vipul: 2 revisions

2008-05-07T23:18:48Z

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Vipul at 08:02, 6 July 2007

2007-07-06T08:02:24Z

← Older revision		Revision as of 08:02, 6 July 2007
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	{{binary operation property}}		{{binary operation property}}

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	==Definition==		==Definition==

Vipul at 12:22, 8 March 2007

2007-03-08T12:22:14Z

New page

{{binary operation property}}

==Definition==

===Definition with symbols===

Let <math>S</math> be a set and <math>*</math> be a binary operation on <math>S</math> (viz, <math>*</math> is a map <math>S</math> × <math>S</math> → <math>S</math>. Then, <math>*</math> is said to be '''commutative''' if, for every <math>a, b, c</math> in <math>S</math>, the following identity holds:

<math>a * b = b * a</math>

If the above equation holds for particular values of <math>a</math> and <math>b</math>, we say that <math>a</math> and <math>b</math> '''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|[[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]].

Commutative binary operation - Revision history

Vipul: 2 revisions

Vipul at 08:02, 6 July 2007

Vipul at 12:22, 8 March 2007