Relative liftings
type: Item
instance of: scholarly article
title: Relative liftings
zbMATH Open document ID: 0872.13013
DOI: 10.1016/0022-4049(94)00106-5
author: Dorin Popescu
published in: Journal of Pure and Applied Algebra
publication date: 1997-09-25T00:00:00Z
review text: Here is the author's abstract: ``Let \((\Lambda,m)\) be a complete Cohen-Macaulay local ring, \(x\) a system of parameters of \(\Lambda\), and \(M\) a finite \(\bar\Lambda:=\Lambda/(x)\)-module. If Ext\(^2_{\bar\Lambda}(M,M)=0\) then there exists a maximal Cohen-Macaulay \(\Lambda\)-module \(L\) such that \(L/xL\cong M\) by a result of Auslander-Ding-Solberg. Here we investigate the problem of finding a generalized Cohen-Macaulay \(\Lambda\)-module \(T\) such that \(T/xT\cong M\). If \(\Lambda\) is regular and \((x)\not=m\), then we hope that our procedure can be useful for some bundle constructions.'' The author develops a theory of weaker forms of liftability than Auslander-Ding-Solberg's: relative, relative\(^\star\) liftability, etc., including infinitesimal versions. The author proves existence theorems for such liftings, and provides examples of modules which are relative\(^\star\) liftable but not liftable.
reviewed by: Moshe Roitman
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13B02
zbMATH DE Number: 897493
zbMATH Keywords: system of parameters
zbMATH Keywords: Cohen-Macaulay local ring
zbMATH Keywords: liftability
zbMATH Keywords: complete local ring
zbMATH Keywords: Koszul complex
zbMATH Keywords: lifting
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)00106-5
OpenAlex ID: W4212973513
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description: scientific article; zbMATH DE number 897493