Injective envelopes and flat covers of modules over a commutative ring
type: Item
instance of: scholarly article
title: Injective envelopes and flat covers of modules over a commutative ring
zbMATH Open document ID: 0853.13009
DOI: 10.1016/0022-4049(95)00085-2
author: Xue Weimin
published in: Journal of Pure and Applied Algebra
publication date: 1996-07-03T00:00:00Z
review text: The author proves the following principal result: Let \(R\) be a commutative semi-local ring with Krull dimension. If \(R\) is an almost noetherian ring, i.e., each non-minimal prime ideal of \(R\) is finitely generated and \(U\) is the minimal injective cogenerator in the category of \(R\)-modules, then the following statements are equivalent: (1) Every \(U\)-reflexive \(R\)-module has a \(U\)-reflexive injective envelope. (2) Every \(U\)-reflexive \(R\)-module has a \(U\)-reflexive flat cover. (3) \(R\) is linear compact and \(\dim (R)\leq 1\).
reviewed by: Iuliu Crivei
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13J99
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 896556
zbMATH Keywords: reflexive module
zbMATH Keywords: linearly compact ring
zbMATH Keywords: almost noetherian ring
zbMATH Keywords: injective envelope
zbMATH Keywords: flat cover
Wikidata QID: Q114215353
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00085-2
OpenAlex ID: W1965062454
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description: scientific article; zbMATH DE number 896556