Cancellation of projective modules over polynomial extensions over a two-dimensional ring
type: Item
instance of: scholarly article
title: Cancellation of projective modules over polynomial extensions over a two-dimensional ring
zbMATH Open document ID: 1400.13013
author: Md. Ali Zinna
published in: Journal of Pure and Applied Algebra
publication date: 2018-10-10T00:00:00Z
review text: Let \(R\) be a commutative Noetherian ring. A finitely generated projective \(R\)-module \(P\) is said to be cancellative if \(P \oplus R^n \cong Q \oplus R^n\) implies \(P \cong Q\). \textit{H. Bass} [Publ. Math., Inst. Hautes Étud. Sci. 22, 489--544 (1964; Zbl 0248.18025)] showed that every finitely generated projective \(R\)-module of rank \(> \dim(R)\) is cancellative. It followed by several researchers such as Suslin, Vaserstein, Bhatwadekar and others. To do this further, the main result of the paper is as follows: Theorem. Let \(R\) be of dimension two with \(1/2 \in R\) and let \(A = R[X_1, \ldots, X_n]\). Let \(P\) be a projective \(A\)-module of rank \(2\). Then \(P\) is cancellative if \(\bigwedge^2(P)\oplus A\) is cancellative.
reviewed by: Majid Eghbali
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13B25
zbMATH DE Number: 6950428
zbMATH Keywords: cancellative modules
zbMATH Keywords: projective modules
MaRDI profile type: Publication
full work available at URL: j.jpaa.2018.04.020
OpenAlex ID: W2800285187
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Wikidata QID: Q129970204
DOI: 10.1016/J.JPAA.2018.04.020
description: scientific article; zbMATH DE number 6950428