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

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

MathSciNet review:
694385

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Abstract | References | Similar Articles | Additional Information

Abstract: A regular semigroup is locally inverse if each local submonoid , 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 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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Additional Information

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

Keywords:
Regular semigroup,
inverse semigroup,
locally testable semigroup,
Rees matrix semigroup,
local submonoid,
local isomorphism

Article copyright:
© Copyright 1983
American Mathematical Society