The structure of pseudo-inverse semigroups

Pastijn, F.

doi:10.1090/S0002-9947-1982-0667165-1

The structure of pseudo-inverse semigroups
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Trans. Amer. Math. Soc. 273 (1982), 631-655 Request permission

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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