Rees matrix covers for locally inverse semigroups

McAlister, D. B.

doi:10.1090/S0002-9947-1983-0694385-3

Rees matrix covers for locally inverse semigroups
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by D. B. McAlister

Trans. Amer. Math. Soc. 277 (1983), 727-738

DOI: https://doi.org/10.1090/S0002-9947-1983-0694385-3

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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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