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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Band decompositions of semigroups


Authors: Mohan S. Putcha and Julian Weissglass
Journal: Proc. Amer. Math. Soc. 33 (1972), 1-7
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9939-1972-0291335-7
MathSciNet review: 0291335
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Abstract: The existence of a band decomposition of a semigroup into semigroups having at most one idempotent and a group ideal whenever it has an idempotent is investigated. It is shown that S has such a band decomposition if and only if, for every c, $ d \in {S^1},a \in S$, the idempotent multiples of cad and $ c{a^2}d$ coincide. The main result is used to characterize those semigroups which are bands of groups, extending a theorem of Clifford.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0291335-7
Keywords: Semigroups, band, group-ideals, nil semigroups
Article copyright: © Copyright 1972 American Mathematical Society