Notes on the graded Jacobson radical: a graded version of the Jacobson stable set

摘要

Let R be an S-graded ring inducing S, that is, a ring which is the direct sum of a family of its additive subgroups indexed by a nonempty set S, under the assumption that the product of homogeneous elements is again homogeneous. We introduce a graded version of the subring and discuss its homogeneity, where U(R) denotes the group of units of R. Communicated by Pavel Kolesnikov