2018/09/13 by Lännström, Daniel
#16S35 #16W50 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1809.04935
Let G be a group and let S=\bigoplusg ∈ G Sg be a G-graded ring. Given a normal subgroup N of G, there is a naturally induced G/N-grading of S. It is well-known that if S is strongly G-graded, then the induced G/N-grading is strong for any N. The class of epsilon-strongly graded rings was recently introduced by Nystedt, Öinert and Pinedo as a generalization of unital strongly graded rings. We give an example of an epsilon-strongly graded partial skew group ring such that the induced quotient group grading is not epsilon-strong. Moreover, we give necessary and sufficient conditions for the induced G/N-grading of an epsilon-strongly G-graded ring to be epsilon-strong. Our method involves relating different types of rings equipped with local units (s-unital rings, rings with sets of local units, rings with enough idempotents) with generalized epsilon-strongly graded rings.