semigroup with involution

An involution on a semigroup $S$ [on a monoid $M$ ] is a unary operation $x\mapsto x^{*}$ defined on $S$ [resp. on $M$ ] such that for each $x,y\in S$ [resp. for each $x,y\in M$ ]

(x^{*})^{*}=x,\ \ \ (xy)^{*}=y^{*}x^{*}.

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].

References

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