Jordan derivations of unital algebras with idempotents

We consider Jordan derivations of a unital algebra A having a nontrivial idempotent. It turns out that on unital algebras there exist Jordan derivations that are not derivations. For this purpose we introduce the term a singular Jordan derivation, which is a proper Jordan derivation of the form that...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 437; no. 9; pp. 2271 - 2284
Main Authors BENKOVIC, Dominik, SIROVNIK, Nejc
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.11.2012
Elsevier
Subjects
Algebra
Antiderivation
Associative rings and algebras
Derivation
Exact sciences and technology
Jordan derivation
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Singular Jordan derivation
Unital algebra
Derivation
16W25
Singular Jordan derivation
Jordan derivation
Unital algebra
Antiderivation
Singularity
Ring
Idempotent matrix
Jordan algebra
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Summary:We consider Jordan derivations of a unital algebra A having a nontrivial idempotent. It turns out that on unital algebras there exist Jordan derivations that are not derivations. For this purpose we introduce the term a singular Jordan derivation, which is a proper Jordan derivation of the form that depends on Peirce decomposition of the unital algebra A. Singular Jordan derivations are usually antiderivations. The main result of the paper states that under certain conditions every Jordan derivation of A is the sum of a derivation and a singular Jordan derivation.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2012.06.009