Generalized twisted group rings of finite groups

Abstract

Let R be a discrete valuation ring and G a finite group. Let alpha : G x G --> R\{0} be a generalized 2-cocycle, i.e. not necessarily taking its values in the units of R, and consider the generalized twisted group ring R *(alpha) G. In this paper we derive a criterion for R *(alpha) G to be separable over its center. This leads us to study the center and the prime ideals of R *(alpha) G. Furthermore, we give some results on indecomposable modules over R *(alpha) G.