The simple modules of certain generalized crossed products

We consider a Dedekind domain D and a Z-graded ring R = + (i is an element of z) R-i with R-0 = D and each R-i = D upsilon(i) being a free D-module of rank 1. The structure of R is described by an automorphism of D and a generalized 2-cocycle c:Z x Z --> D not necessarily taking its values in the units of D. The aim of this paper is to classify the simple R-modules, say in the case where c(i, j) not equal 0 for all i, j is an element of Z. We also deal with this problem in the N-graded case. As a consequence we obtain a description of the simple modules of some classical algebras and of generalized Weyl algebras. (C) 1997 Academic Press.