Geodesic
On group graded rings satisfying polynomial identities
Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 205-210

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Kelarev, A. V.; Okniński, J. On group graded rings satisfying polynomial identities. Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 205-210. doi: 10.1017/S0017089500031104
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