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

Modular congruences and the Brown-McCoy radical for semigroups


Author: D. R. LaTorre
Journal: Proc. Amer. Math. Soc. 29 (1971), 427-433
MSC: Primary 20.93
MathSciNet review: 0280631
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Abstract: The Brown-McCoy radical $ {R_{{G^0}}}$ for semigroups with zero is characterized in terms of modular two-sided congruences. The general notion of the $ \mathcal{C}$-radical of a semigroup is used to prove that $ {R_{{G^0}}}$ is the $ {\rho _s}$-class containing zero, where $ {\rho _s}$ is the intersection of all modular maximal two-sided congruences of S. Thus when $ {\rho _s}$ is the identity relation, $ {R_{{G^0}}} = 0$ and S is isomorphic to a subdirect product of congruence-free semigroups with zero and identity. We also link $ {R_{{G^0}}}$ to representation theory.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0280631-4
PII: S 0002-9939(1971)0280631-4
Keywords: Brown-McCoy radical, congruence-free semigroups, modular congruences, radical theory for semigroups
Article copyright: © Copyright 1971 American Mathematical Society