Her Eş-sonlu Genişlemesinde Zayıf Rad-tümleyene Sahip Modüller

Year 2024, , 379 - 385, 29.02.2024

Emine Önal Kır , Hamza Çalışıcı

https://doi.org/10.2339/politeknik.991518

Abstract

Bu çalışmada, (CWE) ve (CWEE) özelliğine sahip modüllerin bir genelleştirilişi olarak (CWRE) ve (CWREE) özelliğine sahip modülleri tanımlıyoruz. R bir halka ve M sol R-modül olsun. Eğer M (CWRE) özelliğine sahip ise, M modülünün her direkt toplam terimi (CWRE) özelliğine sahiptir. Bir R halkasının yarıyerel olması için gerek ve yeter şart her sol R-modülün (CWRE) özelliğine sahip olmasıdır. Ayrıca (WRE*) ve (WREE*) özelliğine sahip modülleri çalışıyoruz. Bir modülün (WREE*) özelliğine sahip olması için gerek ve yeter şart onun her alt modülünün (WRE*) özelliğine sahip olmasıdır. 

Keywords

Zayıf Rad-tümleyen, yarıyerel halka, eş-sonlu genişleme

Modules Having a Weak Rad-Supplement in Every Cofinite Extension

Abstract

In this study, we introduce the modules with the properties (CWRE) and (CWREE) as a generalization of the modules with the properties (CWE) and (CWEE). Let R be a ring and M be a left R-module. If M has the property (CWRE), then every direct summand of M has the property (CWRE). A ring R is semilocal if and only if every left R-module has the property (CWRE). We also study the modules that have the properties (WRE*) and (WREE*). A module has the property (WREE*) if and only if every submodule of it has the property (WRE*).   

Keywords

Weak Rad-supplement, semilocal ring, cofinite extension

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