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Free Involutorial Completely Simple Semigroups

Published online by Cambridge University Press:  20 November 2018

J. A. Gerhard and
Mario Petrich
J. A. Gerhard
Affiliation:
University of Manitoba, Winnipeg, Manitoba
Mario Petrich
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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An involution x → x* of a semigroup S is an antiautomorphism of S of order at most 2, that is (xy)* = y*x* and x** = x for all x, y ∊ S. In such a case, S is called an involutorial semigroup if regarded as a universal algebra with the binary operation of multiplication and the unary operation *. If S is also a completely simple semigroup, regarded as an algebra with multiplication and the unary operation x → x −1 of inversion (x −1 is the inverse of x in the maximal subgroup of S containing x), then (S, −1, *), or simply S, is an involutorial completely simple semigroup. All such S form a variety determined by the identities above concerning * and

where x 0 = xx −1.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 2 , 01 April 1985, pp. 271 - 295
Copyright
Copyright © Canadian Mathematical Society 1985

References

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