×

On the nilpotency of the Jacobson radical of semigroup rings. (English) Zbl 0822.16015

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.

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
PDFBibTeX XMLCite
Full Text: EuDML EMIS