On Centralizers of 2-torsion Free Semiprime Gamma Rings

Abdulkareem T Mutlak,Abulrahman H Majeed

doi:10.24996/ijs.2021.62.7.23

Abstract

In this paper, we prove that; Let M be a 2-torsion free semiprime which satisfies the condition for all and α, β . Consider that as an additive mapping such that holds for all and α , then T is a left and right centralizer.

Highlights

An extensive generalized concept of classical rings was presented by the gamma ring theory
Bernes [1], Luh [2] and Kyuno [3] studied the structure of gamma rings and obtained various generalizations of corresponding parts in the ring theory
Hoque and Paul [5] proved that every Jordan centralizer of 2-torsion free semiprime is centralizer

Summary

Introduction

An extensive generalized concept of classical rings was presented by the gamma ring theory. Bernes [1], Luh [2] and Kyuno [3] studied the structure of gamma rings and obtained various generalizations of corresponding parts in the ring theory. Let and be additive abelian groups, if there exists a mapping of which satisfies the conditions: i. M is called semiprime if implies where [5]. ) holds for all and α A centralizer is an additive mapping which is both a left and right centralizer [5]

Let M be a

Results

This implies that