## 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)

### Citations:

Zbl 0439.16001; Zbl 0424.16001
Full Text:

### References:

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