Two results concerning symmetric bi-derivations on prime rings
type: Item
instance of: scholarly article
title: Two results concerning symmetric bi-derivations on prime rings
zbMATH Open document ID: 0716.16013
DOI: 10.1007/BF02112294
published in: Aequationes Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137372
review text: Let \(R\) be a prime ring with \(\text{char}(R)\neq 2,3\), and \(D\colon R\times R\to R\) a bi-additive, symmetric map so that \(D(\;,y)\colon R\to R\) is a derivation for all \(y\in R\). The paper proves two results about such mappings, called symmetric bi-derivations. The first assumes that \(D_ 1\) and \(D_ 2\) are symmetric bi-derivations with \(D_ 1(x,x)D_ 2(x,x)=0\) for all \(x\in R\) and proves that \(D_ 1=0\) or \(D_ 2=0\). The second result shows that if \(D\) is a symmetric bi-derivation with \([D(x,x),x]\) central for all \(x\in R\), then either \(R\) is commutative or \(D=0\).
reviewed by: Charles Lanski
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16U80
zbMATH DE Number: 4179581
zbMATH Keywords: prime rings
zbMATH Keywords: bi-additive symmetric maps
zbMATH Keywords: symmetric bi-derivations
author: Joso Vukman
MaRDI profile type: Publication
cites work: Centralizing Mappings of Semiprime Rings
cites work: On some additive mappings in rings with involution
cites work: Q3913817
cites work: Q3781515
cites work: Centralizing Automorphisms of Prime Rings
cites work: Ideals and Centralizing Mappings in Prime Rings
cites work: Centralizing Mappings of Prime Rings
cites work: Derivations in Prime Rings
cites work: Commuting and Centralizing Mappings in Prime Rings
cites work: Symmetric bi-derivations on prime and semi-prime rings
cites work: Q5289831
description: scientific article; zbMATH DE number 4179581