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On group graded rings satisfying polynomial identities

Published online by Cambridge University Press:  18 May 2009

A. V. Kelarev  and
J. Okniński
A. V. Kelarev
Affiliation:
Department of Mathematics, University of Tasmania, Hobart, GPO Box 252C, Tasmania 7001, Australia
J. Okniński
Affiliation:
Department of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
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A number of classical theorems of ring theory deal with nilness and nilpotency of the Jacobson radical of various ring constructions (see [10], [18]). Several interesting results of this sort have appeared in the literature recently. In particular, it was proved in [1] that the Jacobson radical of every finitely generated PI-ring is nilpotent. For every commutative semigroup ring RS, it was shown in [11] that if J(R) is nil then J(RS) is nil. This result was generalized to all semigroup algebras satisfying polynomial identities in [15] (see [16, Chapter 21]). Further, it was proved in [12] that, for every normal band B, if J(R) is nilpotent, then J(RB) is nilpotent. A similar result for special band-graded rings was established in [13, Section 6]. Analogous theorems concerning nilpotency and local nilpotency were proved in [2] for rings graded by finite and locally finite semigroups.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 2 , May 1995 , pp. 205 - 210
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

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