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Journals / Sinop Üniversitesi Fen Bilimleri Dergisi / 2023 / Cilt: 8 Sayı: 2

On ss-Lifting Modules In View of Singularity

Singülerlik Açısından ss-Lifting Modüller

Esra Öztürk Sözen(SİNOP ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0002-2632-2193
Elif Eryaşar(SINOP UNIVERSITY)0000-0002-9852-6662
Pages
145–155
Publication Date
2023-12-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we give several characterizations for (projective) δss-lifting modules and (amply) δss-supplemented modules via δss-perfect rings.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this essay we describe δss-lifting modules as a singular version of ss-lifting ones.
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Key Findings & Data:The focus of this study is to get a more general algebraic structure than ss-lifting modules.
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Conclusion & Impact:Finally, we give several characterizations for (projective) δss-lifting modules and (amply) δss-supplemented modules via δss-perfect rings.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Yarı basit modül · δss-tümlenmi¸s modül · δss-yükseltilebilir modül

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.

Özet

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.

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Cite This Article

Sözen, E. Ö., Eryaşar, E. (2023). On ss-Lifting Modules In View of Singularity. Sinop Üniversitesi Fen Bilimleri Dergisi, Cilt: 8 Sayı: 2, 145–155. https://doi.org/10.33484/sinopfbd.1355648

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