Some cancellation theorems about projective modules over polynomial rings
type: Item
instance of: scholarly article
title: Some cancellation theorems about projective modules over polynomial rings
zbMATH Open document ID: 0639.13006
DOI: 10.1016/0021-8693(87)90247-X
author: Amit Roy
author: S. M. Bhatwadekar
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: Let R be a commutative Noetherian ring of dimension d, \(A=R[X_ 1,...,X_ n]\) and P a finitely generated projective A-module. P is cancellative if \(P\oplus A=Q\oplus A\) implies \(P\cong Q\). The aim of this paper is to give a positive answer when \(d=2\) or \(n=2\) and R is normal to the following question of \textit{H. Bass}: ``Is every projective A-module P of \(rank\geq d+1\) cancellative?'' In an ``Added in proof'' it is announced that the above question was solved positively by R. A. Rao and H. Lindel by different techniques.
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 4042041
zbMATH Keywords: cancellative projective module
zbMATH Keywords: polynomial rings
zbMATH Keywords: unimodular element
MaRDI profile type: Publication
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full work available at URL: 0021-8693(87)90247-x
OpenAlex ID: W2016865893
description: scientific article; zbMATH DE number 4042041