The Simple Modules of Certain Generalized Crossed Products Original Research Article

We consider a Dedekind domainDand aZ-graded ringimagewithR0 = Dand eachRi = Dvibeing a freeD-module of rank 1. The structure ofRis described by an automorphism ofDand a generalized 2-cocyclec : Z × Z → Dnot necessarily taking its values in the units ofD. The aim of this paper is to classify the simpleR-modules, say in the case wherec(i, j) ≠ 0 for alli, j set membership, variant Z. We also deal with this problem in theN-graded case. As a consequence we obtain a description of the simple modules of some classical algebras and of generalized Weyl algebras.