Some decomposition properties of injective and pure-injective modules
type: Item
instance of: scholarly article
title: Some decomposition properties of injective and pure-injective modules
zbMATH Open document ID: 0817.16003
author: José Luis García
author: Nguyen Viet Dung
published in: Osaka Journal of Mathematics
publication date: 1995-06-07T00:00:00Z
review text: Many results are known about injective modules, or generalisations thereof, in the category of modules over a ring. For example there are results concerning the expressibility of such modules as direct sums of indecomposable modules. The theme of this paper is to prove such results for injective objects, or more general objects, in a suitable category. For instance if \(M\) is a sigma-injective object and \(F\) is a CS subobject of \(M\), then \(F\) is a direct sum of indecomposable objects. Also in this categorical context a generalization is given of the Faith-Walker characterization of sigma-injective modules. The authors are thus able to give new proofs of, or to extend, some known results about generalizations of injective modules.
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 639568
zbMATH Keywords: injective modules
zbMATH Keywords: category of modules
zbMATH Keywords: direct sums of indecomposable modules
zbMATH Keywords: sigma-injective modules
zbMATH Keywords: generalizations of injective modules
reviewed by: A. W. Chatters
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 639568