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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The structure of pseudo-inverse semigroups

Author: F. Pastijn
Journal: Trans. Amer. Math. Soc. 273 (1982), 631-655
MSC: Primary 20M10
MathSciNet review: 667165
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Abstract: A regular semigroup $ S$ is called a pseudo-inverse semigroup if $ eSe$ is an inverse semigroup for each $ e = {e^2} \in S$. We show that every pseudo-inverse semigroup divides a semidirect product of a completely simple semigroup and a semilattice. We thereby give a structure theorem for pseudo-inverse semigroups in terms of groups, semilattices and morphisms. The structure theorem which is presented here generalizes several structure theorems which have been given for particular classes of pseudo-inverse semigroups by several authors, and thus contributes to a unification of the theory.

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Keywords: Pseudo-inverse semigroup, proper inverse semigroup, rectangular band of inverse semigroups, pseudo-semilattice, semilattice, order automorphism
Article copyright: © Copyright 1982 American Mathematical Society