Kelarev, A. V. On the nilpotency of the Jacobson radical of semigroup rings. (English) Zbl 0822.16015 Acta Math. Univ. Comen., New Ser. 63, No. 1, 161-166 (1994). Let \(R[S]\) be the semigroup ring of a finitely generated commutative semigroup \(S\) over an associative ring \(R\). It is shown that the nilpotency of the Jacobson radical of \(R\) implies that the Jacobson radical of \(R[S]\) is nilpotent. A characterization of arbitrary commutative semigroups \(S\) such that the above implication holds for every ring \(R\) is also obtained. Reviewer: J.Okniński (Warszawa) Cited in 1 Document MSC: 16N20 Jacobson radical, quasimultiplication 16S36 Ordinary and skew polynomial rings and semigroup rings 20M14 Commutative semigroups 20M25 Semigroup rings, multiplicative semigroups of rings 16N40 Nil and nilpotent radicals, sets, ideals, associative rings Keywords:semigroup ring; finitely generated commutative semigroup; nilpotency; Jacobson radical PDFBibTeX XMLCite \textit{A. V. Kelarev}, Acta Math. Univ. Comen., New Ser. 63, No. 1, 161--166 (1994; Zbl 0822.16015) Full Text: EuDML EMIS