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

⊕-Dual (Eş) Sonlu Radikal Tümlenmiş Modüllerin Genelleştirilmesi

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

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