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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On regular semigroups and their multiplication


Author: Pierre Antoine Grillet
Journal: Trans. Amer. Math. Soc. 246 (1978), 111-138
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9947-1978-0515532-8
MathSciNet review: 515532
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Abstract: A method is given for the construction of regular semigroups in terms of groups and partially ordered sets. This describes any regular semigroup S and its multiplication by means of triples $ \left( {i,\,g,\,\lambda } \right)$ with $ i\, \in \,S/{\mathcal{R}}$, $ \lambda \, \in \,S/{\mathcal{L}}$ and g in the Schützenberger group of the corresponding $ {\mathcal{D}}$-class. It is shown that the multiplication on S is determined by certain simple products. Furthermore the associativity of these simple products implies associativity of the entire multiplication.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0515532-8
Article copyright: © Copyright 1978 American Mathematical Society