Some Results on δ-Semiperfect Rings and δ-Supplemented Modules

- Journal title : Kyungpook mathematical journal
- Volume 55, Issue 2, 2015, pp.289-300
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2015.55.2.289

Title & Authors

Some Results on δ-Semiperfect Rings and δ-Supplemented Modules

ABDIOGLU, CIHAT; SAHINKAYA, SERAP;

ABDIOGLU, CIHAT; SAHINKAYA, SERAP;

Abstract

In [9], the author extends the definition of lifting and supplemented modules to -lifting and -supplemented by replacing "small submodule" with "-small submodule" introduced by Zhou in [13]. The aim of this paper is to show new properties of -lifting and -supplemented modules. Especially, we show that any finite direct sum of -hollow modules is -supplemented. On the other hand, the notion of amply -supplemented modules is studied as a generalization of amply supplemented modules and several properties of these modules are given. We also prove that a module M is Artinian if and only if M is amply -supplemented and satisfies Descending Chain Condition (DCC) on -supplemented modules and on -small submodules. Finally, we obtain the following result: a ring R is right Artinian if and only if R is a -semiperfect ring which satisfies DCC on -small right ideals of R.

Keywords

-small submodules;-supplemented modules;-lifting modules;amply -supplemented modules;

Language

English

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