Tensor products of perfect modules and maximal surjective Buchsbaum modules
type: Item
instance of: scholarly article
title: Tensor products of perfect modules and maximal surjective Buchsbaum modules
zbMATH Open document ID: 0901.13010
DOI: 10.1016/S0022-4049(96)00088-6
author: Ken-Ichi Yoshida
published in: Journal of Pure and Applied Algebra
publication date: 1998-11-19T00:00:00Z
review text: Let \(A\) be a Cohen-Macaulay (shortly CM) local ring and \(M\) a finite \(A\)-module with finite \(\text{pd}_AM\). Then \(M\) is perfect iff \(M\otimes_AN\) is a CM \(A\)-module with \(\dim M\otimes_AN=\dim M\) for some (resp. any) maximal CM \(A\)-module \(N\). This result extends a Kawasaki result [cf. \textit{T. Kawasaki}, Math. Z. 218, No. 2, 191-205 (1995; Zbl 0814.13017)] obtained for the case when \(N\) is a canonical module of \(A\). Moreover if \(M\) is perfect and \(N\) is a maximal surjective Buchsbaum \(A\)-module then \(M\otimes_AN\) is Buchsbaum, \(\dim M\otimes_AN= \dim M\) and \(\text{depth }M\otimes_AN= \max\{\text{depth }N- \text{pd}_AM,0\}\).
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D05
zbMATH DE Number: 1121672
zbMATH Keywords: Cohen-Macaulay modules
zbMATH Keywords: Buchsbaum modules
zbMATH Keywords: local cohomology modules
zbMATH Keywords: perfect module
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1121672