Generalized twisted group rings

Abstract

Let R be a dornain and G a group. Let alpha: G x G -> R \ {0} be a generalized 2-cocycle, i.e., not necessarily taking its values ill the units of R, and consider the generalized twisted group ring R *(alpha) G. First we investigate the graded structure of R *(alpha) G, in particular we give conditions under which R *(alpha) G is gr-hereditary, respectively a gr-maximal order. Next, we derive criteria for R *(alpha) G to be a tame order, respectively a maximal order over some central subring. We also derive conditions under which R *(alpha) G is an Azumaya algebra. (c) 2005 Elsevier Inc. All rights reserved.