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When is R-gr equivalent to the category of modules? (English) Zbl 0657.16025

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 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.
Reviewer: R.Gordon

MSC:

16D90 Module categories in associative algebras
16W50 Graded rings and modules (associative rings and algebras)
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References:

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