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Proceedings of the American Mathematical Society

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

 

 

On the structure of idempotent semigroups


Author: R. J. Warne
Journal: Proc. Amer. Math. Soc. 37 (1973), 17-21
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9939-1973-0306380-3
MathSciNet review: 0306380
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Abstract: An idempotent semigroup (band) is a semigroup in which every element is an idempotent. We describe the structure of idempotent semigroups in terms of semilattices $ \Omega $, partial chains $ \Omega $ of left zero semigroups, and partial chains $ \Omega $ of right zero semigroups. We also describe bands of maximal left zero semigroups in terms of partial chains $ \Omega $ of left zero semigroups and semilattices $ \Omega $ of right zero semigroups.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0306380-3
Keywords: Idempotent semigroup, band of left zero semigroups, band, semilattice, semilattice of right zero semigroups
Article copyright: © Copyright 1973 American Mathematical Society