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Proceedings of the American Mathematical Society

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

 

 

Semilattice of bisimple regular semigroups


Author: H. R. Krishna Iyengar
Journal: Proc. Amer. Math. Soc. 28 (1971), 361-365
MSC: Primary 20.93
DOI: https://doi.org/10.1090/S0002-9939-1971-0274624-0
MathSciNet review: 0274624
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Abstract: The main purpose of this paper is to show that a regular semigroup $ S$ is a semilattice of bisimple semigroups if and only if it is a band of bisimple semigroups and that this holds if and only if $ \mathcal{D}$ is a congruence on $ S$. It is also shown that a quasiregular semigroup $ S$ which is a rectangular band of bisimple semigroups is itself bisimple.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0274624-0
Keywords: Quasiregular, rectangular band, semilattice, Baer-Levi semigroup, congruence
Article copyright: © Copyright 1971 American Mathematical Society