semigroup with involution
An involution on a semigroup S [on a monoid M] is a unary operation x↦x* defined on S [resp. on M] such that for each x,y∈S [resp. for each x,y∈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 |