Divisibility and duo-rings
type: Item
instance of: scholarly article
title: Divisibility and duo-rings
zbMATH Open document ID: 1448.16001
DOI: 10.4171/RSMUP/40
author: Bradley McQuaig
author: Ulrich F. Albrecht
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2020-07-13T00:00:00Z
review text: Let \(R\) be a right non-singular ring with maximal right ring of quotients \(Q\). This paper addresses the question of when the projective dimension pd\(_R(Q)\leq 1\) implies that \(Q/R\) is a direct sum of countable modules. That property allows several notions in the literature of divisibility concerning modules over integral domains to be extended to the non-commutative case. For example, the authors study the relations between the following properties of a module \(D\): \begin{itemize} \item for all regular \(c\in R,\ Dc=D\); \item \(D\) is the epimorphic image of an injective module; \item for all \(r\in R,\ \mathrm{Ext}_R^1(R/rR,\, D)=0\). \end{itemize}
reviewed by: Phillip Schultz
Mathematics Subject Classification ID: 16D10
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16S85
zbMATH DE Number: 7219813
zbMATH Keywords: divisible
zbMATH Keywords: duo-rings
zbMATH Keywords: pre-Matlis
MaRDI profile type: Publication
cites work: Right Utumi p.p.-rings.
cites work: Torsion-freeness and non-singularity over right p.p.-rings.
cites work: COTILTING CLASSES OF TORSION-FREE MODULES
cites work: Abelian groups without elements of finite order
cites work: Tilting Cotorsion Pairs
cites work: Q3325883
cites work: Three questions on duo rings
cites work: Relative homological algebra
cites work: ON MODULES OVER COMMUTATIVE RINGS
cites work: Q4513600
cites work: Approximations and endomorphism algebras of modules.
cites work: Q4104083
cites work: A Foundation of Torsion Theory for Modules Over General Rings
cites work: The Third Axiom of Countability for Abelian Groups
cites work: Divisible modules and localization
cites work: Q5515432
cites work: On divisible modules over domains
cites work: Divisible Modules
cites work: Q3882615
cites work: An introduction to homological algebra
description: scientific article; zbMATH DE number 7219813