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semigroups with commuting idempotents

Proceedings of the Edinburgh Mathematical Society (1)

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REES MATRIX COVERS FOR A CLASS OF SEMIGROUPS WITH LOCALLY COMMUTING IDEMPOTENTS
Tanveer A. Khan, Mark V. Lawson
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 44 / Issue 1 / February 2001

Published online by Cambridge University Press:

20 January 2009, pp. 173-186
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McAlister proved that every regular locally inverse semigroup can be covered by a regular Rees matrix semigroup over an inverse semigroup by means of a homomorphism which is locally an isomorphism. We generalize this result to the class of semigroups with local units whose local submonoids have commuting idempotents and possessing what we term a ‘McAlister sandwich function’.
AMS 2000 Mathematics subject classification: Primary 20M10. Secondary 20M17