Let G be a group and let S = circle plus(g is an element of G) S-g 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 et al. 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.
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