The structure of dualizing complex for a ring which is \((S_2)\)
type: Item
instance of: scholarly article
title: The structure of dualizing complex for a ring which is \((S_2)\)
zbMATH Open document ID: 0949.13010
published in: Journal of Mathematics of Kyoto University
publication date: 2000-02-03T00:00:00Z
review text: Let \(A\) be a commutative noetherian ring. Assume that \(A\) has a fundamental dualizing complex, using an appropriate filtration of \(\text{Spec}(A)\), it is shown that the Cousin complex of the canonical module \(K\) associate to this filtration is isomorphic to the fundamental dualizing complex when \(\text{Min}(A)= \text{Ass}_A(K)\) and \(A\) is \((S_2)\). As applications, the authors show that: (i) if \(A\) is a ring which is \((S_2)\) and has a fundamental dualizing complex, the injective envelope \(E(A/{\mathfrak p})\) for \({\mathfrak p}\in\text{Spec}(A)\) is described using generalized fractions; (ii) if \((A,{\mathcal M})\) is a local ring which is \((S_2)\) and has a canonical module \(K\), if \(K\) is a generalized Cohen-Macaulay module then \(A\) is generalized Cohen Macaulay and it has a dualizing complex.
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 13B30
zbMATH DE Number: 1309657
zbMATH Keywords: fundamental dualizing complex
zbMATH Keywords: Cousin complex
zbMATH Keywords: generalized Cohen-Macaulay module
zbMATH Keywords: canonical module
zbMATH Keywords: filtration
zbMATH Keywords: \(S_2\)
zbMATH Keywords: injective envelope
zbMATH Keywords: generalized fractions
author: Mohammad T. Dibaei
author: Massoud Tousi
reviewed by: Blas Torrecillas
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518063
OpenAlex ID: W2100479867
DOI: 10.1215/KJM/1250518063
description: scientific article; zbMATH DE number 1309657