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semigroup with involution (Definition)

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$]

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

Bibliography

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



"semigroup with involution" is owned by Mazzu.
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See Also: I-semigroup, Thue system

Other names:  *-semigroup
Also defines:  involution, semigroup with involution, monoid with involution
Keywords:  semigroup

Attachments:
free semigroup with involution (Example) by Mazzu
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Cross-references: operation, unary, monoid, semigroup
There are 13 references to this entry.

This is version 4 of semigroup with involution, born on 2006-08-23, modified 2006-08-24.
Object id is 8281, canonical name is SemigroupWithInvolution.
Accessed 2138 times total.

Classification:
AMS MSC: 20M10 (Group theory and generalizations :: Semigroups :: General structure theory)
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