Abstract
We consider a Dedekind domainDand aZ-graded ringR=;⊕i∈ZRiwithR0=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∈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.
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