On ss-Lifting Modules In View of Singularity

Abstract

In this essay we describe δss-lifting modules as a singular version of ss-lifting ones. The focus of this study is to get a more general algebraic structure than ss-lifting modules. A module W is entitled δss-lifting if for each S ≤ W, there occurs a decomposition W = X ⊕ Y with X ≤ S and S ∩ Y ≤ Socδ(Y ), where Socδ(Y ) = δ(Y ) ∩ Soc(Y ). We examine the fundamental properties of this form of modules and also investigate a structure of a ring whose modules are all δss-lifting. Finally, we give several characterizations for (projective) δss-lifting modules and (amply) δss-supplemented modules via δss-perfect rings.

Keywords

• Semisimple module
• δss-supplemented module
• δss-lifting module
• Left δss-perfect ring

Singülerlik Açısından ss-Lifting Modüller

Abstract

Bu makalede ss-yükseltilebilir modüllerin singüler versiyonu olan δss-yükseltilebilir modülleri tanımlıyoruz. Çalışmanın amacı δss-yükseltilebilir modüllerden daha genel bir cebirsel yapı elde etmektir. Bir W modülü, her S ≤ W alt modülü için, Socδ(Y ) = δ(Y ) ∩ Soc(Y ) olmak üzere, X ≤ S ve S ∩ Y ≤ Socδ(Y ), koşullarını gerçekleyen W = X ⊕ Y ayrışımına sahip ise W’ya δss-yükseltilebilir modül denir. Bu modüllerin temel özelliklerini araştırıyor ve üzerindeki her modülü δss-yükseltilebilir olan bir halka yapısı arıyoruz. Sonunda ise, δss-mükemmel halkalar aracılığı ile (projektif) δss-yükseltilebilir ve (bol) δss-tümlenmiş modüllerin bir takım karakterizasyonlarını veriyoruz.

Keywords

• Yarı basit modül
• δss-tümlenmi¸s modül
• δss-yükseltilebilir modül
• Sol δss-mükemmel halka

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