⊕-Dual (Eş) Sonlu Radikal Tümlenmiş Modüllerin Genelleştirilmesi

Year 2024, Volume: 9 Issue: 1, 36 - 43, 29.06.2024

Şeyma Haldız , Figen Eryılmaz

https://doi.org/10.33484/sinopfbd.1381635

Abstract

Bu makalede ⊕−dual sonlu radikal tümleyen modüllerin genellemesi olarak maksimal alt modülleri ⊕−radikal tümleyene sahip modüller (𝑚𝑔𝑠⊕) tanımlandı ve bu modülün bazı temel özellikleri incelendi. Keyfi bir 𝑚𝑔𝑠⊕−modülünün bölüm modülünün hangi şartlar altında 𝑚𝑔𝑠⊕−modül olduğu gösterildi ve yarı mükemmel halkalar bu modül yardımıyla karakterize edildi.

Keywords

Maksimal alt modül, radikal tümleyen, ⊕−dual sonlu radikal tümlenmiş modül

Generalization of ⊕-Cofinitely Radical Supplemented Modules

Abstract

In this study, we clarify 𝑚𝑔𝑠⊕−modules that are the generalization of ⊕−cofinitely radical supplemented modules and look at some of their basic characteristics. Additionally, we determine the prerequisites for the factor module of an arbitrary 𝑚𝑔𝑠⊕−module to be a 𝑚𝑔𝑠⊕−module and characterized semiperfect rings with the aid of this module.

Keywords

Maximal submodule, Rad-supplement, ⊕−cofinitely radical supplemented module

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