Free resolutions and change of rings
type: Item
instance of: scholarly article
title: Free resolutions and change of rings
zbMATH Open document ID: 0879.13007
published in: Journal of Algebra
publication date: 1997-05-27T00:00:00Z
review text: The author constructs a projective resolution \(F(X,Y)\) of a module \(M\) over a ring \(R\), starting from appropriate projective resolutions, \(X\) of \(R\) and \(Y\) of \(M\), over a ring \(Q\) mapping to \(R\). It is shown that such resolutions may be chosen to be minimal in codimension \(\leq 2\), but not in codimension 3. This is used to obtain minimal resolutions for essentially all modules over local (or graded) rings \(R\) with codimension \(\leq 2\). Explicit resolutions are given for cyclic modules over multigraded rings, and necessary and sufficient conditions are obtained for their minimality.
Mathematics Subject Classification ID: 13D25
zbMATH DE Number: 1013971
zbMATH Keywords: projective resolution
zbMATH Keywords: codimension
zbMATH Keywords: cyclic modules
author: Srikanth B. Iyengar
reviewed by: Iuliu Crivei
MaRDI profile type: Publication
OpenAlex ID: W2153711812
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DOI: 10.1006/JABR.1996.6901
description: scientific article; zbMATH DE number 1013971