GRADED EQUIVALENCE THEORY WITH APPLICATIONS

We develop the foundations for graded equivalence theory and apply the m to investigate properties such as primeness, finite representation t ype, and vertex theory of graded rings. The key fact that we prove is that, for any two G-graded rings R and S such that there is a category equivalence from gr(R) to gr(S) that commutes with suspensions, then, for any subgroup H of G, the categories gr(H/G, R) and gr(H/G, S) of modules graded by the G-set of right cosets are also equivalent. (C) 1 995 Academic Press, Inc.