Morita equivalence of semigroups with local units |
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Authors: | MV Lawson |
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Institution: | Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland, United Kingdom |
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Abstract: | We prove that two semigroups with local units are Morita equivalent if and only if they have a joint enlargement. This approach to Morita theory provides a natural framework for understanding McAlister’s theory of the local structure of regular semigroups. In particular, we prove that a semigroup with local units is Morita equivalent to an inverse semigroup precisely when it is a regular locally inverse semigroup. |
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Keywords: | Primary 20M10 Secondary 20M17 20M50 |
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