Abstract
We develop the foundations for graded equivalence theory and apply them to investigate properties such as primeness, finite representation type, 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.
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