Gamma-derivations in prime and semiprime gamma-near-rings
type: Item
instance of: scholarly article
title: Gamma-derivations in prime and semiprime gamma-near-rings
zbMATH Open document ID: 1017.16041
author: Yong Uk Cho
author: Young Bae Jun
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2003-03-20T00:00:00Z
review text: Let \(M\) be a (right) \(\Gamma\)-near ring. A \(\Gamma\)-derivation of \(M\) is an additive endomorphism \(d\) of \(M\) satisfying \(d(x\gamma y)=x\gamma d(y)+d(x)\gamma y\) for all \(x,y\in M\) and \(\gamma\in\Gamma\). A \(\Gamma\)-derivation is said to act as a \(\Gamma\)-homomorphism on a subset \(S\) of \(M\) if \(d(x\gamma y)=d(x)\gamma d(y)\) for all \(x,y\in S\). It is shown that if \(M\) is semiprime, \(A\) is a left invariant subset of \(M\) containing \(0\), and \(\Gamma\)-derivation \(d\) acts as a \(\Gamma\)-homomorphism on \(A\), then \(d(A)=0\). Moreover, if \(M\) is a prime \(\Gamma\)-near-ring, \(A\) is a left invariant subset of \(M\) containing \(0\) and \(d\) acts as a \(\Gamma\)-homomorphism on \(A\), then \(d=0\).
Mathematics Subject Classification ID: 16Y99
Mathematics Subject Classification ID: 16W25
zbMATH DE Number: 1874245
zbMATH Keywords: \(\Gamma\)-near rings
zbMATH Keywords: \(\Gamma\)-derivations
zbMATH Keywords: additive endomorphisms
zbMATH Keywords: \(\Gamma\)-homomorphisms
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1874245