This paper is about QI-modules M and the full subcategory σ[M] of Mod-R subgenerated by M. A ring R is a right QI-ring if every quasi-injective right R-module is injective. The module M is QI if all quasi-injective modules in σ[M] are M-injective. Three classes of rings are presented for each of which the QI-modules are precisely the semisimple modules. The QI-modules M are characterized in terms of properties of some lattices of classes of modules in σ[M].
KeywordsDirect Summand Module Class Subdirect Product Natural Class Boolean Lattice
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