Non-finitely generated projective modules over generalized Weyl algebras.
type: Item
instance of: scholarly article
title: Non-finitely generated projective modules over generalized Weyl algebras.
zbMATH Open document ID: 1167.16001
author: Pavel Příhoda
author: Gena Puninski
published in: Journal of Algebra
publication date: 2009-04-29T00:00:00Z
review text: 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.
reviewed by: Vyacheslav A. Artamonov
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16S32
zbMATH DE Number: 5549362
zbMATH Keywords: infinitely generated projective modules
zbMATH Keywords: generalized Weyl algebras
zbMATH Keywords: rings of differential operators
zbMATH Keywords: direct sums
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.11.015
OpenAlex ID: W1994783354
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DOI: 10.1016/J.JALGEBRA.2008.11.015
description: scientific article; zbMATH DE number 5549362