WEAKLY LOCALLY ARTINIAN SUPPLEMENTED MODULES

Abstract

In this study, by using the concept of locally artinian supplemented modules, we have obtained that weakly locally artinian supplemented modules as a proper generalization of these modules in module theory. Our results generalize and extend various comparable results in the existing literature. We have proved that a notion of weakly locally artinian supplemented modules inherited by factor modules, finite sums and small covers. We have obtained that weakly locally artinian supplemented modules with small radical coincide with weakly (radical) supplemented modules which have locally artinian radical. Also, we have shown that if $N$ and $\frac{M}{N}$ are weakly locally artinian supplemented for some submodule $N\subseteq M$ which has a weak locally artinian supplement in $M$ then $M$ is weakly locally artinian supplemented.

Keywords

• Locally artinian module
• (weak) supplement
• (weak) locally artinian supplement
• (weakly) locally artinian supplemented module

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