Groups, semilattices and inverse semigroups. I, II

McAlister, D. B.

doi:10.1090/S0002-9947-1974-0357660-2

Groups, semilattices and inverse semigroups. I, II
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by D. B. McAlister

Trans. Amer. Math. Soc. 192 (1974), 227-244

DOI: https://doi.org/10.1090/S0002-9947-1974-0357660-2

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Abstract:

An inverse semigroup S is called proper if the equations $ea = e = {e^2}$ together imply ${a^2} = a$ for each a, $a,e \in S$. In this paper a construction is given for a large class of proper inverse semigroups in terms of groups and partially ordered sets; the semigroups in this class are called P-semigroups. It is shown that every inverse semigroup divides a P-semigroup in the sense that it is the image, under an idempotent separating homomorphism, of a full subsemigroup of a P-semigroup. Explicit divisions of this type are given for $\omega$-bisimple semigroups, proper bisimple inverse semigroups, semilattices of groups and Brandt semigroups.

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