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- W93831494 abstract "An R-module is called semi-endosimple if it has no proper fully invariant essential submodules. For a quasi-projective retractable module MR we show that M is finitely generated semi-endosimple if and only if the endomorphism ring of M is a finite direct sum of simple rings. For an arbitrary module M, conditions equivalent to the semi-endosimplicity of its quasi-injective hull are found. As consequences of these results, new characterizations of V-rings, right Noetherian V-rings and strongly semiprime rings are obtained. As such, a hereditary left Noetherian ring R is a finite direct sum of simple Noetherian right V-rings if and only if all finitely generated right R-modules are semi-endosimple. Mathematics Subject Classification: 16D10, 16D40, 16D90" @default.
- W93831494 created "2016-06-24" @default.
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- W93831494 date "2009-01-01" @default.
- W93831494 modified "2023-09-27" @default.
- W93831494 title "Semi-Endosimple Modules and Some Applications" @default.
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