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GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS

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

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 [email protected]
RUTH N. FERREIRA
Affiliation:
Universidade Tecnológica Federal do Paraná, Avenida Professora Laura Pacheco Bastos, 800, 85053-510 Guarapuava, Brazil email [email protected]
HENRIQUE GUZZO Jr.
Affiliation:
Universidade de São Paulo, Rua do Matão, 1010, 05508-090 São Paulo, Brazil email [email protected]
*
✉[email protected]
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Abstract

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.

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References

Brešar, M., ‘Jordan derivations on semiprime rings’, Proc. Amer. Math. Soc. 104 (1988), 1003–1006.Google Scholar
Călugăreanu, G., ‘A new class of semiprime rings’, Houston J. Math. 44 (2018), 21–30.Google Scholar
Herstein, I. N., ‘Jordan derivations of prime rings’, Proc. Amer. Math. Soc. 8 (1957), 1104–1110.Google Scholar
Jacobson, N., Structure of Rings, American Mathematical Society Colloquium Publications, 37 (American Mathematical Society, Providence, RI, 1964).Google Scholar
Jing, W. and Lu, S., ‘Generalized Jordan derivations on prime rings and standard operator algebras’, Taiwanese J. Math. 7 (2003), 605–613.Google Scholar