CATEGORIES OF MODULES GRADED BY G-SETS - APPLICATIONS

This paper studies rings R graded by a G-set X such that the category of X-graded left R-modules, (G,X,R)-gr, is equivalent to A-mod, A a ri ng with 1. Examples of such rings, other than strongly graded rings, e xist. For every infinite group G, there is a G-graded ring R such that (G, G,R)-gr = R-gr is equivalent to A-mod, for some A with 1, but R c ontains no strongly graded subring except R(e). The find section gives connections between some properties of R and R, for such rings.