A monoid is a semigroupPlanetmathPlanetmath G which contains an identity elementMathworldPlanetmath; that is, there exists an element eG such that ea=ae=a for all aG.

If e and f are identity elements of a monoid G, then e=ef=fe=f, so we may speak of “the” identity element of G.

A monoid homomorphism from monoids G to H is a semigroup homomorphism f:GH such that f(eG)=eH, where eG,eH are identity elements of G and H respectively.

Title monoid
Canonical name Monoid
Date of creation 2013-03-22 11:50:15
Last modified on 2013-03-22 11:50:15
Owner djao (24)
Last modified by djao (24)
Numerical id 9
Author djao (24)
Entry type Definition
Classification msc 20M99
Classification msc 34-01
Synonym homomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath
Related topic Semigroup
Defines monoid homomorphism