The Source of Semi-Primeness of Γ-Rings

Author:

ARSLAN Okan1ORCID,DÜZKAYA Nurcan2ORCID

Affiliation:

1. Aydın Adnan Menderes Üniversitesi, Fen Fakültesi, Matematik Bölümü

2. AYDIN ADNAN MENDERES ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ, MATEMATİK (YL) (TEZLİ)

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.

Publisher

Fundamentals of Contemporary Mathematical Sciences

Reference11 articles.

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.

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1. The Source of $\Gamma$-Primeness on $\Gamma$-Rings;Mathematical Sciences and Applications E-Notes;2024-01-28

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