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Groups, Semilattices and Inverse Semigroups

D. B. McAlister
Transactions of the American Mathematical Society
Vol. 192 (May, 1974), pp. 227-244
DOI: 10.2307/1996831
Stable URL: http://www.jstor.org/stable/1996831
Page Count: 18
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Groups, Semilattices and Inverse Semigroups
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Abstract

An inverse semigroup S is called proper if the equations ea = e = e2 together imply a2 = a for each a, e ∈ 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 ω-bisimple semigroups, proper bisimple inverse semigroups, semilattices of groups and Brandt semigroups.

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