ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES

Abstract

The aim of this paper is to investigate generalizations of locally artinian supplemented modules in module theory, namely locally artinian radical supplemented modules and strongly locally artinian radical supplemented modules. We have obtained elementary features for them. Also, we have characterized strongly locally artinian radical supplemented modules by left perfect rings. Finally, we have proved that the reduced part of a strongly locally artinian radical supplemented $R$-module has the same property over a Dedekind domain $R$.

Keywords

• Locally artinian module
• (Locally artinian) supplement
• (strongly) locally artinian radical supplemented module
• Left perfect ring
• Dedekind domain

References

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