Radicals of semigroup rings
- 1 July 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 10 (2) , 85-93
- https://doi.org/10.1017/s0017089500000616
Abstract
Let denote the contracted semigroup ring of the ompletely 0-simple semigroup D over the ring R. The Rees structure theory of completely 0-simple semigroups is used to obtain necessary and sufficient conditions that have zero radical (Theorem 3.8). By using Amitsur's construction of the upper π-radical [1], we are able to treat the Jacobson, Baer (prime), Levitzki (locally nilpotent) and possibly the nil radicals simultaneously. Our results generalize a theorem of Munn [6] on semigroup algebras of finite 0-simple semigroups.Keywords
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