On some radicals and proper classes associated to simple modules

Septimiu Crivei; Derya Keskin Tütüncü

Septimiu Crivei
Derya Keskin Tütüncü

Keywords: Radical, Proper class, Simple module, Relative supplement submodule, M-injective module, M-projective module, M-small module, M-singular module

Abstract

For a unitary right module $M$, there are two known partitions of simple modules in the category $\sigma[M]$: the first one divides them into $M$-injective modules and $M$-small modules, while the second one divides them into $M$-projective modules and $M$-singular modules. We study inclusions between the first two and the last two classes of simple modules in terms of some associated radicals and proper classes.

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