On coretractable modules
type: Item
instance of: scholarly article
title: On coretractable modules
zbMATH Open document ID: 1352.16005
author: D. Keskin-Tütüncü
author: Berke Kaleboğaz
published in: Hokkaido Mathematical Journal
publication date: 2016-01-29T00:00:00Z
review text: A right \(R\)-module \(M\) is called: (i) coretractable if \(\text{Hom}_R(M/K,M)\neq 0\) for every proper submodule \(K\) of \(M\); (ii) mono-coretractable if there is a monomorphism from \(M/K\) to \(M\) for every submodule \(K\) of \(M\). The authors prove that every right \(R\)-module is coretractable if and only if \(R\) is right perfect, and every right \(R\)-module is small coretractable if and only if all torsion theories on \(R\) are cohereditary. They also show that coretractable modules are a proper generalization of mono-coretractable modules.
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16D80
zbMATH DE Number: 6537499
zbMATH Keywords: coretractable module
zbMATH Keywords: Kasch module
reviewed by: Iuliu Crivei
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1470052355
OpenAlex ID: W2475581642
DOI: 10.14492/HOKMJ/1470052355
description: scientific article; zbMATH DE number 6537499