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Transactions of the American Mathematical Society

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

 

 

Groups, semilattices and inverse semigroups. II


Author: D. B. McAlister
Journal: Trans. Amer. Math. Soc. 196 (1974), 351-370
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9947-74-99950-4
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Abstract: An inverse semigroup is called proper if the equations $ ae = e = {e^2}$ together imply $ {a^2} = 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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DOI: https://doi.org/10.1090/S0002-9947-74-99950-4
Keywords: Inverse semigroup, proper inverse semigroup, semilattice, idempotent separating congruence, fundamental inverse semigroup, group action, order automorphisms
Article copyright: © Copyright 1974 American Mathematical Society