On some radicals and proper classes associated to simple modules

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.

Keywords

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

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