The Source of Semi-Primeness of Γ-Rings

Year 2023, Volume: 4 Issue: 2, 87 - 95, 31.07.2023

Okan Arslan , Nurcan Düzkaya

https://doi.org/10.54974/fcmathsci.1203544

Cited By: 1

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.

Keywords

$\Gamma$-ring, source of semi-primeness, strong unity

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