A semigroupPlanetmathPlanetmath G is a set together with a binary operationMathworldPlanetmath :G×GG which satisfies the associative property: (ab)c=a(bc) for all a,b,cG.

The set G is not required to be nonempty.

Let G,H be two semigroups. A semigroup homomorphism from G to H is a function f:GH such that f(ab)=f(a)f(b).

Title semigroup
Canonical name Semigroup
Date of creation 2013-03-22 11:50:08
Last modified on 2013-03-22 11:50:08
Owner djao (24)
Last modified by djao (24)
Numerical id 11
Author djao (24)
Entry type Definition
Classification msc 20M99
Synonym homomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath
Related topic groupoidPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath
Related topic Band2
Related topic SubmonoidSubsemigroup
Related topic NullSemigroup
Related topic ZeroElements
Related topic Monoid
Defines semigroup homomorphism