SS-supplemented modules

Year 2020, Volume: 69 Issue: 1, 473 - 485, 30.06.2020

Engin Kaynar , Ergül Türkmen Hamza Çalışıcı

https://doi.org/10.31801/cfsuasmas.585727

Cited By: 17

https://izlik.org/JA94KE44DZ

Abstract

A module M is called ss-supplemented if every submodule U of M has a

supplement V in M such that U(intersection)  V is semisimple. It is shown that a finitely generated

module M is ss-supplemented if and only if it is supplemented and Rad(M) (submodule) Soc(M). A module

M is called strongly local if it is local and Rad(M) (submodule)  Soc(M). Any direct sum of strongly

local modules is ss-supplemented and coatomic. A ring R is semiperfect and Rad(R) (submodule)

Soc(_RR) if and only if  every left R-module is ss-supplemented if and only if _RR is a finite sum of strongly local

submodules.

Keywords

strongly local module , semisimple module , ss-supplemented module

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