Counterinjective modules and duality
type: Item
instance of: scholarly article
title: Counterinjective modules and duality
zbMATH Open document ID: 0687.16021
DOI: 10.1016/0022-4049(89)90011-X
author: José L. Gómez-Pardo
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: The main object of the paper is counterinjective modules, i.e. modules which are injective over their endomorphism rings. The results obtained are applied to faithfully balanced bimodules and rings with Morita duality. For example, it is shown that for a faithfully balanced bimodule \({}_ RU_ T\) such that \({}_ RU\) and \(U_ T\) are injective and the class of modules of U-dom dim \(\geq 2\) is closed under directed unions, then the ring R has left Morita duality. Further, some known characterizations of QF-rings are extended to faithfully balanced bimodules, using the notation of \(\Sigma\)-injectivity or \(\Delta\)- injectivity. Finally, necessary and sufficient conditions are obtained for a quasi-injective module \({}_ RU\) to be an injective cogenerator over its endomorphism ring.
reviewed by: Dinh Van Huynh
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 4125616
zbMATH Keywords: counterinjective modules
zbMATH Keywords: endomorphism rings
zbMATH Keywords: faithfully balanced bimodules
zbMATH Keywords: left Morita duality
zbMATH Keywords: QF-rings
zbMATH Keywords: \(\Sigma\)-injectivity
zbMATH Keywords: \(\Delta\)- injectivity
zbMATH Keywords: quasi-injective module
zbMATH Keywords: injective cogenerator
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4125616