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Journals / Fundamentals of Contemporary Mathematical Sciences / 2023 / Volume: 4 Issue: 2

The Source of Semi-Primeness of Γ-Rings

Okan Arslan(Aydın Adnan Menderes Üniversitesi, Fen Fakültesi, Matematik Bölümü)0000-0002-1006-066X
Nurcan Düzkaya(AYDIN ADNAN MENDERES ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ, MATEMATİK (YL) (TEZLİ))0000-0003-0733-3572
Pages
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Publication Date
2023-07-31
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AI Summary & Key Takeaways

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

We determined all possible characteristic values of a SSMS -domain and proved every finite SSMS -domain Γ-ring M is a SSMS -division Γ-ring.

📌 3 Key Takeaways

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Objective & Hypothesis:The notion of source of semi-primeness is firstly given by Aydın, Demir and Camcı in 2018 as the set of all elements a of R that satisfy aRa 􀀀 0 for any associative ring R.
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Key Findings & Data:The theory of gamma ring has been introduced by Nobusawa in 1964 as a generalization of rings.
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Conclusion & Impact:We determined all possible characteristic values of a SSMS -domain and proved every finite SSMS -domain Γ-ring M is a SSMS -division Γ-ring.
🔬Design:Research Article
📍Scope:2018 Verileri
⚙️Variables:$\Gamma$-ring · source of semi-primeness · strong unity

Abstract

The notion of source of semi-primeness is firstly given by Aydın, Demir and Camcı in 2018 as the set of all elements a of R that satisfy aRa 􀀀 0 for any associative ring R. They investigated some basic properties of this set and defined three types of rings which have not appeared in literature before. The theory of gamma ring has been introduced by Nobusawa in 1964 as a generalization of rings. In this work, we generalized the notion of source of semi-primeness for gamma rings and investigated its basic algebraic properties. We also defined SSMS -strongly reduced Γ-ring, SSMS -domain, SSMS -division ring and examined the relationship between these structures. We determined all possible characteristic values of a SSMS -domain and proved every finite SSMS -domain Γ-ring M is a SSMS -division Γ-ring.

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Cite This Article

Arslan, O., Düzkaya, N. (2023). The Source of Semi-Primeness of Γ-Rings. Fundamentals of Contemporary Mathematical Sciences, Volume: 4 Issue: 2. https://doi.org/10.54974/fcmathsci.1203544

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References (11)

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