Characterizing Jordan \(n\)-derivations of unital rings containing idempotents
type: Item
instance of: scholarly article
title: Characterizing Jordan \(n\)-derivations of unital rings containing idempotents
zbMATH Open document ID: 1473.16034
author: N. E. Zubov
published in: Bulletin of the Iranian Mathematical Society
publication date: 2021-01-05T00:00:00Z
review text: Let \(R\) be a ring. For \(x,y\in R\) write \(\{x,y\}=xy+yx\). Further, define \(p_1(x)=x\) and \(p_n(x_1,\dots,x_n)= \{p_{n-1}(x_1,\dots,x_{n-1}),x_n\}\) for \(n\ge 2\). The authors call a not necessarily additive map \(\delta:R\to R\) a Jordan \(n\)-derivation if it satisfies \[\delta(p_n(x_1,\dots,x_n)) = \sum_{i=1}^n p_n(x_1,\dots,x_{i-1}, \delta(x_i),x_{i+1},\dots,x_n)\] for all \(x_i\in R\). It is shown that \(\delta\) is necessarily additive if \(R\) contains an idempotent that satisfies certain technical conditions. Moreover, under slightly stronger assumptions, \(\delta\) is a Jordan derivation.
reviewed by: Matej Brešar
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16U40
zbMATH DE Number: 7290384
zbMATH Keywords: Jordan \(n\)-derivation
zbMATH Keywords: ring
zbMATH Keywords: idempotent
MaRDI profile type: Publication
full work available at URL: s41980-019-00348-7
OpenAlex ID: W2998883594
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Wikidata QID: Q126319052
DOI: 10.1007/S41980-019-00348-7
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description: scientific article; zbMATH DE number 7290384