A.D. Bell: Abstract

Prime Ideals and Radicals in Rings Graded by Clifford Semigroups


Allen D. Bell

Publication Information

Appeared in Communications in Algebra 25#5 (1997), pp. 1595-1608
Math Reviews: 98e:16022

Abstract (in LaTex)

In this paper we continue our study of the ideal structure
of the direct sum of a directed system of rings indexed by
a semigroup begun in "Prime Ideals and Radicals in
Semigroup-graded Rings" (with S. Stalder and M. Teply),
with emphasis on describing the prime ideals and radicals of
semigroup rings and semigroup-graded rings. This time we
concentrate on semigroups that fail to satisfy condition
$(\dag)$ of our orginal article but have a sufficient quantity
of nearly central idempotents, and we reduce the description
of the prime ideals and radicals to the case of group rings
and prime families over systems of group rings.
Our results apply to Clifford semigroups, commutative
semigroups for which every element has a power lying in a
subgroup, and some more general classes of semigroups.

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