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Proceedings of the American Mathematical Society

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

 

 

Regularity of semigroup rings


Author: Julian Weissglass
Journal: Proc. Amer. Math. Soc. 25 (1970), 499-503
MSC: Primary 20.90
MathSciNet review: 0257251
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Abstract: The conditions under which a semigroup ring is regular (in the sense of von Neumann) are investigated. Sufficient conditions are obtained in order that the semigroup ring of an inverse semigroup be regular. Consequences of the regularity of the semigroup ring for the subgroups of the semigroup are established. The two results are then used to find necessary and sufficient conditions for the regularity of the semigroup ring when the semigroup is inverse and a union of groups.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0257251-X
Keywords: Regular ring, semigroup ring, contracted semigroup ring, group ring, inverse semigroup, Rees matrix semigroup, completely 0-simple semigroup
Article copyright: © Copyright 1970 American Mathematical Society