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On the Jacobson Radical of Semigroup Graded Rings

✍ Scribed by M.V. Clase; E. Jespers

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 861 KB
Volume: 169
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1994.1273

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✦ Synopsis

We study the Jacobson radical of semigroup graded rings. We show that the Jacobson radical of a ring graded by a (locally) finite semigroup is (locally) nilpotent if the same is true of each homogeneous component corresponding to an idempotent semigroup element and that a ring graded by a finite semigroup is a Jacobson ring if each idempotent graded component is a Jacobson ring. As an application of graded results we prove that a PI semigroup algebra is a Jacobson ring provided that all homomorphic images of the semigroup have finite rank. (0) 1994 Academic Press. Inc.

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