Some Properties of $\oplus -$ Cofinitely $\delta -$s Supplemented Modules

Year 2019, Volume: 9 Issue: 2, 303 - 313, 30.12.2019

Figen Eryılmaz

https://doi.org/10.37094/adyujsci.476813

Abstract

In
this paper, we study the properties generalized $\oplus -$ cofinitely $\delta
-$ supplemented modules or briefly  $\oplus -gcof_{\delta
}-$ supplemented modules. We show that any direct sum of $\oplus
-gcof_{\delta}- $ supplemented modules is a  $\oplus -gcof_{\delta }-$ supplemented
module. If $M$ is a $\oplus -gcof_{\delta }-$ supplemented module with
SSP, then every direct summand of $M$ is $\oplus -gcof_{\delta }-$ supplemented.

Keywords

$\ \delta -$small submodule, $\delta -$supplemented module, cofinite submodule, $\oplus -$ cofinitely supplemented module

Dual Sonlu Tümlenmiş Modüllerin Bazı Özellikleri

Abstract

Bu çalışmada, genelleştirilmiş dual sonlu tümlenmiş modüllerin özellikleri çalışıldı. Bu modüller kısaca  ile gösterildi. Genelleştirilmiş dual sonlu tümlenmiş modüllerin keyfi toplamının da genelleştirilmiş dual sonlu tümlenmiş modül olduğu gösterildi.  modülünün direkt toplam terimlerinin toplama özelliğine sahip (DDT) genelleştirilmiş dual sonlu tümlenmiş bir modül olması durumunda  modülünün her bir direkt toplam teriminin de genelleştirilmiş dual sonlu tümlenmiş modül olduğu ispatlandı.

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