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 $\mathrm{*}$-semigroup [resp. a monoid with involution or $\mathrm{*}$-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 |