Uniserial rings
type: Item
instance of: scholarly article
title: Uniserial rings
zbMATH Open document ID: 0596.16018
DOI: 10.1007/BF01137462
author: I. V. Bobylev
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: R is an associative ring with 1, all R-modules are assumed to be unital. Let M be a right R-module and \(S=End M\) the endomorphism ring of M. If M is S-projective, then M is called an endoprojective right R-module. The author shows that a semisimple ring R, over which each injective right module is endoprojective, is Artinian. He then describes the rings R, such that each right R-module (resp. each quasi-injective right R-module) is endoprojective. It turns out that these rings R are primarily decomposable Artinian semichain rings in the terminology of \textit{C. Faith} [Algebra: Rings, modules and categories (1973; Zbl 0266.16001)].
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16P20
zbMATH DE Number: 3959696
zbMATH Keywords: endomorphism ring
zbMATH Keywords: endoprojective right R-module
zbMATH Keywords: semisimple ring
zbMATH Keywords: injective right module
zbMATH Keywords: quasi-injective right R-module
zbMATH Keywords: primarily decomposable Artinian semichain rings
MaRDI profile type: Publication
cites work: Projective modules
cites work: Noninjective Cyclic Modules
cites work: Q5682108
cites work: Commutative rings whose homomorphic images are self-injective
cites work: Q4071917
cites work: Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
cites work: A generalization of quasi-Frobenius rings
cites work: Rings whose Modules are Projective over Endomorphism Rings
full work available at URL: https://doi.org/10.1007/bf01137462
OpenAlex ID: W4256146709
description: scientific article; zbMATH DE number 3959696