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A Characterisation of a Class of Semigroups with Locally Commuting Idempotents

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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.

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Authors and Affiliations

  1. School of Mathematics, University of Wales, Bangor Dean Street, Bangor, Gwynedd, LL57 1UT, United Kingdom

    Tanveer A. Khan

  2. School of Mathematics, University of Wales, Bangor Dean Street, Bangor, Gwynedd, LL57 1UT, United Kingdom

    Mark V. Lawson

Authors
  1. Tanveer A. Khan
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  2. Mark V. Lawson
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Khan, T.A., Lawson, M.V. A Characterisation of a Class of Semigroups with Locally Commuting Idempotents. Periodica Mathematica Hungarica 40, 85–107 (2000). https://doi.org/10.1023/A:1010327307672

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  • DOI: https://doi.org/10.1023/A:1010327307672

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