KaydedilenlerDerginizi ekleyin

Dergiler / 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
Sayfa
—
Yayın Tarihi
2023-07-31
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri:The theory of gamma ring has been introduced by Nobusawa in 1964 as a generalization of rings.
💡
Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:2018 Verileri
⚙️Değişkenler:$\Gamma$-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.

🔖

Bu Makaleye Atıf Yap

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

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (11)

  1. Aydın N., Demir C., Camcı D.K., The source of semiprimeness of rings, Communications of the Korean Mathematical Society, 33(4), 1083-1096, 2018.
  2. Barnes W., On the Γ -rings of Nobusawa, Pacific Journal of Mathematics, 18(3), 411-422, 1966.
  3. Coppage W.E., Luh J., Radicals of gamma rings, Journal of the Mathematical Society of Japan, 23(1), 40-52, 1971.
  4. Kandamar H., The k-derivation of a Gamma-ring, Turkish Journal of Mathematics, 23(3), 221-229, 2000.
  5. Kyuno S., On the radicals of Γ-rings, Osaka Journal of Mathematics, 12(3), 639-645, 1975.
  6. Kyuno S., On prime gamma rings, Pacific Journal of Mathematics, 75(1), 185-190, 1978.
  7. Kyuno S., Gamma Rings, Hadronic Press, Inc., 1991.
  8. Kyuno S., A gamma ring with minimum conditions, Tsukuba Journal of Mathematics, 5(1), 47-65, 1981.
  9. Luh J., On the theory of simple Γ-rings, The Michigan Mathematical Journal, 16(1), 65-75, 1969.
  10. McCoy N.H., The Theory of Rings, MacMillan, 1968.
  11. Nobusawa N., On a generalization of the ring theory, Osaka Journal of Mathematics, 1(1), 81-89, 1964.