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Mathematica Slovaca

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Volume 62, Issue 3 (Jun 2012)

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On generalized (θ, φ)-derivations in semiprime rings with involution

Mohammad Ashraf
  • Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
  • Email:
/ Nadeem-ur-Rehman
  • Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
  • Email:
/ Shakir Ali
  • Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
  • Email:
/ Muzibur Mozumder
  • Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
  • Email:
Published Online: 2012-05-06 | DOI: https://doi.org/10.2478/s12175-012-0021-1

Abstract

The main purpose of this paper is to prove the following result: Let R be a 2-torsion free semiprime *-ring. Suppose that θ, φ are endomorphisms of R such that θ is onto. If there exists an additive mapping F: R → R associated with a (θ, φ)-derivation d of R such that F(xx*) = F(x)θ(x*) + φ(x)d(x*) holds for all x ∈ R, then F is a generalized (θ, φ)-derivation. Further, some more related results are obtained.

MSC: Primary 16W10; Secondary 16W25, 16N60

Keywords: semiprime ring; involution; derivation; (θ,φ)-derivation; generalized derivation; generalized (θ, φ)-derivation; generalized Jordan (θ,φ)-derivation

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About the article

Published Online: 2012-05-06

Published in Print: 2012-06-01


Citation Information: Mathematica Slovaca, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-012-0021-1. Export Citation

© 2012 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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