On some radicals and proper classes associated to simple modules

Year 2017, Volume: 4 Issue: 2 (Special Issue: Noncommutative rings and their applications), 123 - 129, 10.01.2017

Septimiu Crivei , Derya Keskin Tütüncü

https://doi.org/10.13069/jacodesmath.284943

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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