Counterinjective modules and duality
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.
scientific article; zbMATH DE number 4125616
scientific article