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GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS

Part of: Special classes of linear operators Rings and algebras with additional structure

Published online by Cambridge University Press:  29 July 2019

BRUNO L. M. FERREIRA ,
RUTH N. FERREIRA  and
HENRIQUE GUZZO Jr.
BRUNO L. M. FERREIRA*
Affiliation:
Universidade Tecnológica Federal do Paraná, Avenida Professora Laura Pacheco Bastos, 800, 85053-510 Guarapuava, Brazil email brunoferreira@utfpr.edu.br
RUTH N. FERREIRA
Affiliation:
Universidade Tecnológica Federal do Paraná, Avenida Professora Laura Pacheco Bastos, 800, 85053-510 Guarapuava, Brazil email ruthnascimento@utfpr.edu.br
HENRIQUE GUZZO Jr.
Affiliation:
Universidade de São Paulo, Rua do Matão, 1010, 05508-090 São Paulo, Brazil email guzzo@ime.usp.br
*
✉brunoferreira@utfpr.edu.br
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Abstract

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The purpose of this note is to prove the following. Suppose $\mathfrak{R}$ is a semiprime unity ring having an idempotent element $e$ ($e\neq 0,~e\neq 1$) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathfrak{R}$ is a generalized derivation.

Keywords

Jordan derivationgeneralized Jordan derivationrings

MSC classification

Primary: 16W25: Derivations, actions of Lie algebras
Secondary: 47B47: Commutators, derivations, elementary operators, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 109 , Issue 1 , August 2020 , pp. 36 - 43
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

References

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