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Abstract
We analyze conditions under which an (ungraded) module over a semigroup-graded ring can be embedded in a graded module. We use this information to provide some sufficient conditions under which the graded Jacobson radical of the ring is contained in the (ungraded) Jacobson radical. These include, and give an alternate approach to, the case of group-graded rings.
*This article was written while the second author was a member of G.N.S.A.G.A. of C.N.R. with partial financial support from M.U.R.S.T.
ACKNOWLEDGMENT
The authors extend their thanks to Angel del Río for his many important discussions regarding the results contained in this paper, and to the referee for a helpful and extremely careful reading of the original version of this manuscript.
Notes
*This article was written while the second author was a member of G.N.S.A.G.A. of C.N.R. with partial financial support from M.U.R.S.T.