The theory of local homology for Artinian modules
type: Item
instance of: scholarly article
title: The theory of local homology for Artinian modules
zbMATH Open document ID: 0988.13012
published in: Southeast Asian Bulletin of Mathematics
publication date: 2001-03-19T00:00:00Z
review text: The authors develop the theory of local homology for an Artinian module \(A\) over a commutative ring \(R\) with identity with respect to the following concepts: Starting from an ideal \({\mathfrak a}\subset R\) and its \({\mathfrak a}\)-adic completion functor the authors study \({\mathfrak a}\)-cotorsion modules and \({\mathfrak a}\)-cotorsion-free modules under the Matlis duality functor and give conditions on \(R\) and \(A\) such that the zero submodule of the local homology module \(H_i^{\mathfrak a}(A)\) has a primary decomposition. Moreover they introduce the dual of the ideal transform functor and obtain some results analogous to those of the ideal transform functor.
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 13D45
zbMATH DE Number: 1533393
zbMATH Keywords: filter cosequences
zbMATH Keywords: cotorsion modules
zbMATH Keywords: Artinian module
zbMATH Keywords: local homology module
author: Mohammad T. Dibaei
author: Kamran Divaani-Aazar
MaRDI profile type: Publication
full work available at URL: s10012-000-0031-8
OpenAlex ID: W2071970645
DOI: 10.1007/S10012-000-0031-8
description: scientific article; zbMATH DE number 1533393