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Transactions of the American Mathematical Society

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



Rees matrix covers for locally inverse semigroups

Author: D. B. McAlister
Journal: Trans. Amer. Math. Soc. 277 (1983), 727-738
MSC: Primary 20M15; Secondary 20M10
MathSciNet review: 694385
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Abstract: A regular semigroup $ S$ is locally inverse if each local submonoid $ eSe$, $ e$ an idempotent, is an inverse semigroup. It is shown that every locally inverse semigroup is an image of a regular Rees matrix semigroup, over an inverse semigroup, by a homomorphism $ \theta $ which is one-to-one on each local submonoid; such a homomorphism is called a local isomorphism. Regular semigroups which are locally isomorphic images of regular Rees matrix semigroups over semilattices are also characterized.

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Keywords: Regular semigroup, inverse semigroup, locally testable semigroup, Rees matrix semigroup, local submonoid, local isomorphism
Article copyright: © Copyright 1983 American Mathematical Society