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Groups, Semilattices and Inverse Semigroups. II

D. B. McAlister
Transactions of the American Mathematical Society
Vol. 196 (Sep., 1974), pp. 351-370
DOI: 10.2307/1997032
Stable URL: http://www.jstor.org/stable/1997032
Page Count: 20
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Groups, Semilattices and Inverse Semigroups. II
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Abstract

An inverse semigroup is called proper if the equations ae = e = e2 together imply a2 = a. In a previous paper, with the same title, the author proved that every inverse semigroup is an idempotent separating homomorphic image of a proper inverse semigroup. In this paper a structure theorem is given for all proper inverse semigroups in terms of partially ordered sets and groups acting on them by order automorphisms. As a consequence of these two theorems, and Preston's construction for idempotent separating congruences on inverse semigroups, one can give a structure theorem for all inverse semigroups in terms of groups and partially ordered sets.

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