A note on Jordan triple higher *-derivations on semiprime rings.
type: Item
instance of: scholarly article
title: A note on Jordan triple higher *-derivations on semiprime rings.
zbMATH Open document ID: 1298.16026
DOI: 10.1155/2014/365424
author: O. H. Ezzat
published in: ISRN Algebra
publication date: 2014-06-16T00:00:00Z
review text: Let \(R\) be a 6-torsion free semiprime ring with involution *. The author extends the definitions of Jordan higher derivation and Jordan triple higher derivation to rings with involution. Let \(D=(d_n)\) for \(n\geq 0\) be a sequence of additive maps of \(R\) with \(d_0=\text{id}_R\). Then \(D\) is a Jordan higher *-derivation of \(R\) when for any \(n\geq 1\) and all \(x\in R\), \(d_n(x^2)=\sum_{i+j=n}d_i(x)d_j(x^{*^i})\), and \(D\) is a Jordan triple higher *-derivation of \(R\) when for any \(n\geq 1\) and all \(x,y\in R\), \(d_n(xyx)=\sum_{i+j+k=n}d_i(x)d_j(y^{*^i})d_k(x^{*^{i+j}})\). The main results of the paper show that \(D\) is a Jordan higher *-derivation of \(R\) if and only if \(D\) is a Jordan triple higher *-derivation of \(R\).
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 6304836
zbMATH Keywords: rings with involution
zbMATH Keywords: semiprime rings
zbMATH Keywords: additive maps
zbMATH Keywords: Jordan triple higher *-derivations
zbMATH Keywords: Jordan higher derivations
Wikidata QID: Q59047388
reviewed by: Charles Lanski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/365424
OpenAlex ID: W1979225244
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description: scientific article; zbMATH DE number 6304836