On generalized semiderivations of prime near rings
type: Item
instance of: scholarly article
title: On generalized semiderivations of prime near rings
zbMATH Open document ID: 1441.16050
DOI: 10.1155/2015/867923
author: Abdelkarim Boua
author: A. Raji
author: Asma Ali
author: Farhat Ali
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2018-05-25T00:00:00Z
review text: Summary: Let \(N\) be a near ring. An additive mapping \(F : N \rightarrow N\) is said to be a generalized semiderivation on \(N\) if there exists a semiderivation \(d : N \rightarrow N\) associated with a function \(g : N \rightarrow N\) such that \(F(x y) = F(x) y + g(x) d(y) = d(x) g(y) + x F(y)\) and \(F(g(x)) = g(F(x))\) for all \(x, y \in N\). In this paper we prove that prime near rings satisfying identities involving semiderivations are commutative rings, thereby extending some known results on derivations, semiderivations, and generalized derivations. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a 3-prime near ring \(N\).
Mathematics Subject Classification ID: 16Y30
zbMATH DE Number: 6873269
Wikidata QID: Q59109864
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/867923
OpenAlex ID: W2180395184
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DBLP publication ID: journals/ijmmsc/BouaRAA15
description: scientific article; zbMATH DE number 6873269