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semigroup with involution
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(Definition)
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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].
- 1
- J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, Oxford, 1991.
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"semigroup with involution" is owned by Mazzu.
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See Also: I-semigroup, Thue system
| Also defines: |
involution, semigroup with involution, monoid with involution |
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Cross-references: operation, unary, monoid, semigroup
There are 16 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 3851 times total.
Classification:
| AMS MSC: | 20M10 (Group theory and generalizations :: Semigroups :: General structure theory) |
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Pending Errata and Addenda
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