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Let  G  be a group, and  A  a  G -graded ring. Motivated by the study of densely group graded algebras, we introduce the concept of a pseudo-strongly graded ring associated to an Ore set in this paper. A pseudo-strongly graded ring is a weak version of a strongly graded ring. It induces an equivalence of certain quotient categories.

Pseudo-strongly graded rings associated to Ore sets