A Generalized Higher Reverse Left (respectively Right) Centralizer on Prime Gamma-Rings

Fawaz Ra'ad Jarullah ,Salah Mehdi Salih

doi:10.7176/mtm/9-10-06

Abstract

This study introduces the concepts of generalized higher reverse left (respectively right) centralizer , Jordan generalized higher reverse left (respectively right) centralizer and Jordan triple generalized higher reverse left (respectively right) centralizer of Gamma-rings. In this paper we prove the following main results . Every Jordan generalized higher reverse left (respectively right) ............. Mathematic Subject classification : 16N60 , 16W25 , 16Y99 DOI: 10.7176/MTM/9-10-06 Publication date: October 31 st 2019

Highlights

Let M and be two additive a belian groups
If M is a -ring, [ x,y ] = x y – y x, for all x, y M and,is known as a commutator . [ 5 ] An additive mapping d : M ⎯→ M is called a derivation if the following holds : d( x y ) = d( x ) y + x d( y ), for all x, y M and [ 2 ]
Since M is a 2-torsion free -ring, we obtain that F is a Jordan triple generalized higher reverse left centralizer of M

Summary

Introduction

Let M and be two additive a belian groups. Suppose that there is a mapping from M M ⎯→ M (the image of ( x , , y ) denoted by x y, where x , y M and ) satisfying the following properties for all x , y , z M and , (i) ( x + y ) z = x z + y z x( + )z=x z+x z x (y + c) = x y + x z (ii) (x y ) z = x ( y z ). Let t = ( ti ) i N be a family of additive mappings of a -ring M into itself . t is called a Jordan higher reverse left (respectively right ) centralizer of M if the following equation holds : n tn (x α x) = t i (x) α t i -1(x) i=1 n

Results

Conclusion