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A Characterisation of a Class of Semigroups with Locally Commuting Idempotents |
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| Authors: | Khan Tanveer A. Lawson Mark V. |
| Affiliation: | (1) School of Mathematics, University of Wales, Bangor Dean Street, Bangor, Gwynedd, LL57 1UT, United Kingdom;(2) School of Mathematics, University of Wales, Bangor Dean Street, Bangor, Gwynedd, LL57 1UT, United Kingdom |
| Abstract: | McAlister proved that a necessary and sufficient condition for a regular semigroup S to be locally inverse is that it can be embedded as a quasi-ideal in a semigroup T which satisfies the following two conditions: (1) T = TeT, for some idempotent e; and (2) eTe is inverse. We generalise this result to the class of semigroups with local units in which all local submonoids have commuting idempotents. |
| Keywords: | Semigroups with local units semigroups in which the idempotents in each local submonoid commute enlargements |
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