commutative semigroup

A semigroupPlanetmathPlanetmath S is commutativePlanetmathPlanetmathPlanetmath if the defining binary operationMathworldPlanetmath is commutative ( That is, for all x,yS, the identityPlanetmathPlanetmathPlanetmathPlanetmath xy=yx holds.

Although the term Abelian semigroup is sometimes used, it is more common simply to refer to such semigroups as commutative semigroups.

A monoid which is also a commutative semigroup is called a commutative monoid.

Title commutative semigroup
Canonical name CommutativeSemigroup
Date of creation 2013-03-22 13:08:09
Last modified on 2013-03-22 13:08:09
Owner mclase (549)
Last modified by mclase (549)
Numerical id 4
Author mclase (549)
Entry type Definition
Classification msc 20M14
Synonym Abelian semigroup
Related topic AbelianGroup
Related topic AbelianGroup2
Defines commutative
Defines commutative monoid