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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Right group congruences on a semigroup


Author: Francis E. Masat
Journal: Proc. Amer. Math. Soc. 50 (1975), 107-114
MSC: Primary 20M10
MathSciNet review: 0372085
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Abstract: This paper develops necessary and sufficient conditions on an algebraic semigroup $ S$ in order that it will have nontrivial right group homomorphic images. A central notion used is that of how the normal subsemigroups associated with the group images of $ S$ relate to the right group images of $ S$. The results presented thus extend those of R. R. Stoll. Where right group congruences exist, the structure of $ S$ is determined and the right group congruences are characterized in terms of group congruences and right zero congruences on $ S$. Sufficient conditions are then found for the existence of a minimum right group congruence on $ S$, and isomorphic right group congruences and the minimum right group congruence on $ S$ are described. Lastly, an application is made to regular semigroups whose idempotents form a rectangular band.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0372085-8
PII: S 0002-9939(1975)0372085-8
Keywords: Right group congruences, ideal decompositions, orthodox semigroups, right zero congruences, normal subsemigroups, group congruences
Article copyright: © Copyright 1975 American Mathematical Society