When is R-gr equivalent to the category of modules? (Q1110639)

Let G be a group. Several necessary and sufficient conditions are given for the category, R-gr, of graded modules over a G-graded ring R to be equivalent to a module category. One condition is that R-gr have a finitely generated generator; another is that R-gr is equivalent to S-gr for some strongly G-graded ring S. Also, an example is given of a non- strongly G-graded ring R such that R-gr is equivalent to \(R_ 1\)-mod. This is in contrast to \textit{E. C. Dade}'s result [Math. Z. 174, 241-262 (1980; Zbl 0424.16001)] which asserts that G-graded R is strongly graded if and only if the functor \(R\otimes_{R_ 1}\)-: \(R_ 1\)-mod\(\to R\)-gr is an equivalence.