Regularity of Semigroup Rings

1 July 1970

journal article
Published by JSTOR in Proceedings of the American Mathematical Society

Vol. 25 (3) , 499-503
https://doi.org/10.2307/2036629

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.

Keywords

This publication has 6 references indexed in Scilit:

Radicals of semigroup rings
Glasgow Mathematical Journal, 1969
The Algebraic Theory of Semigroups, Vol. I. By A. H. Clifford and G. B. Preston. Pp. xv + 224. $10.60. 1961. (American Mathematical Society, Providence.)
The Mathematical Gazette, 1964
Continuous Geometry. By John von Neumann. Princeton Mathematical Series, No. 25. With a foreword by Israel Halperin. Pp. xiv + 299. 45s. 1960. (Princeton University Press. London: Oxford University Press)
The Mathematical Gazette, 1963
On the Group Ring
Canadian Journal of Mathematics, 1963
On Regular Group Rings
Proceedings of the American Mathematical Society, 1957
A note on inverse semigroups
Mathematical Proceedings of the Cambridge Philosophical Society, 1955