semigroup with involution

An involution on a semigroup S [on a monoid M] is a unary operation xx* defined on S [resp. on M] such that for each x,yS [resp. for each x,yM]


With this added internal operation, the semigroup S [resp. the monoid M] becomes a semigroup with involution or *-semigroup [resp. a monoid with involution or *-monoid].


  • 1 J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, Oxford, 1991.
Title semigroup with involution
Canonical name SemigroupWithInvolution
Date of creation 2013-03-22 16:11:24
Last modified on 2013-03-22 16:11:24
Owner Mazzu (14365)
Last modified by Mazzu (14365)
Numerical id 7
Author Mazzu (14365)
Entry type Definition
Classification msc 20M10
Synonym *-semigroup
Related topic ISemigroup
Related topic ThueSystem
Defines involution
Defines semigroup with involution
Defines monoid with involution