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The structure of completely regular semigroups


Author: Mario Petrich
Journal: Trans. Amer. Math. Soc. 189 (1974), 211-236
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9947-1974-0330331-4
MathSciNet review: 0330331
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Abstract: The principal result is a construction of completely regular semigroups in terms of semilattices of Rees matrix semigroups and their translational hulls. The main body of the paper is occupied by considerations of various special cases based on the behavior of either Green's relations or idempotents. The influence of these special cases on the construction in question is studied in considerable detail. The restrictions imposed on Green's relations consist of the requirement that some of them be congruences, whereas the restrictions on idempotents include various covering conditions or the requirement that they form a subsemigroup.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0330331-4
Keywords: Completely regular semigroups, orthodox semigroups, bands of groups, semilattices of groups, translational hull, completely simple semigroups, rectangular groups, classification of semigroups
Article copyright: © Copyright 1974 American Mathematical Society

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