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1	Arity
1	Operation
1	Semigroup
2	Monoid

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Semigroup With Involution

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

$\displaystyle (x^*)^*=x,\ \ \ (xy)^*=y^*x^*.$

With this added internal operation, the semigroup

[resp. the monoid

] becomes a semigroup with involution or

-semigroup [resp. a monoid with involution or

-monoid].

Bibliography

1: J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, Oxford, 1991.