Jordan Left Derivation and Centralizer on Skew Matrix Gamma Ring

Rajaa C Shaheen

doi:10.24996/ijs.2021.62.5.26

Abstract

We define skew matrix gamma ring and describe the constitution of Jordan left centralizers and derivations on skew matrix gamma ring on a -ring. We also show the properties of these concepts.

Highlights

The linear ring mapping from onto is called a left derivation (LD ) (resp., Jordan left derivation (JLD)) if=x (y)+y (x) x,y
Bresar and Vukman [2] introduced the concept of left derivation .We refer the readers to several references [3,4, 5, 6] for results concerning Jordan left derivations
On a skew matrix ring being Jordan derivation. He proved that there exist many Jordan derivation maps of it, which are not derivations maps

Summary

1-Introduction

The linear ring mapping from onto is called a left derivation (LD ) (resp., Jordan left derivation (JLD)) if (xy)=x (y)+y (x) x,y . In [10 ], Hamaguchi provided the sufficient and necessary conditions for J on a skew matrix ring being Jordan derivation. He proved that there exist many Jordan derivation maps of it, which are not derivations maps. He studied the characterization of derivation on skew matrix ring In this article ,we define the skew matrix gamma ring as follows. We shall describe the constitution of JLD on skew matrix gamma ring

We choose and

Let J be a JLC of