Non-finitely generated projective modules over generalized Weyl algebras.
Let \(R\) be a Noetherian ring in which every descending chain of ideals \(I_1\supset I_2\supset\cdots\) such that \(I_{k+1}I_k=I_{k+1}\) stabilizes. There is found a criterion under which each projective module is a direct sum of finitely generated ones. In particular, let \(A\) be a generalized Weyl algebra in the sense of V. Bavula. It is shown that any infinitely generated projective \(A\)-module is a direct sum of some homogeneous left ideals and some modules from a specific finite set of projective modules.
scientific article; zbMATH DE number 5549362
scientific article