On the Jacobson radical of graded rings. (English) Zbl 0765.16013

Kelarev, A. V.

Commentat. Math. Univ. Carol. 33, No. 1, 21-24 (1992).

Let \(S\) be a commutative semigroup. Then the Jacobson radical \(J(R)\) of each semigroup-graded ring \(R=\sum_{s\in S} R_ s\) satisfies the formula \(J(R)=\sum_{s\in S}(J(R)\cap R_ s)\) if and only if \(S\) is embeddable in a torsion-free abelian group.

Reviewer: M.L.Teply (Milwaukee)

MSC:

16W50	Graded rings and modules (associative rings and algebras)
16N20	Jacobson radical, quasimultiplication
20M25	Semigroup rings, multiplicative semigroups of rings
20M14	Commutative semigroups
16S35	Twisted and skew group rings, crossed products

Keywords:

\(S\)-homogeneous; cancellative; commutative semigroup; Jacobson radical; semigroup-graded ring