Generalized Jordan derivations on semiprime rings

Feng Wei; Zhankui Xiao

doi:10.1515/dema-2007-0405

Generalized Jordan derivations on semiprime rings

Feng Wei
, Zhankui Xiao

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

It is shown that, given a 2-torsion-free semiprime ring with unit e, every generalized Jordan derivation on R is a generalized derivation. Let n be a fixed positive integer, R be a noncommutative (n + 1)!-torsion-free prime ring with the center C_R. It is proved that, if μ : R → R is a generalized Jordan derivation of R such that μ(x)xⁿ + xⁿμ{x) ∈ C_R for all x ∈ R, then μ = 0.

Original language	English
Pages (from-to)	789-798
Number of pages	10
Journal	Demonstratio Mathematica
Volume	40
Issue number	4
DOIs	https://doi.org/10.1515/dema-2007-0405
Publication status	Published - Oct 2007

Keywords

Generalized Jordan derivations

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10.1515/dema-2007-0405

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abstract = "It is shown that, given a 2-torsion-free semiprime ring with unit e, every generalized Jordan derivation on R is a generalized derivation. Let n be a fixed positive integer, R be a noncommutative (n + 1)!-torsion-free prime ring with the center CR. It is proved that, if μ : R → R is a generalized Jordan derivation of R such that μ(x)xn + xnμ\{x) ∈ CR for all x ∈ R, then μ = 0.",

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AB - It is shown that, given a 2-torsion-free semiprime ring with unit e, every generalized Jordan derivation on R is a generalized derivation. Let n be a fixed positive integer, R be a noncommutative (n + 1)!-torsion-free prime ring with the center CR. It is proved that, if μ : R → R is a generalized Jordan derivation of R such that μ(x)xn + xnμ{x) ∈ CR for all x ∈ R, then μ = 0.

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Generalized Jordan derivations on semiprime rings

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