Mediterranean Journal of Mathematics

, Volume 12, Issue 1, pp 1–7 | Cite as

On Generalized α-Biderivations

  • Ajda Fošner


We determine the structure of a generalized α-biderivation of a noncommutative prime ring \({\mathcal{R}}\) . Moreover, we also consider the case when the ring \({\mathcal{R}}\) is semiprime.

Mathematics Subject Classification (2010)

16W20 16W25 16N60 


Prime ring semiprime ring biderivation α-biderivation generalized biderivation generalized α-biderivation 


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  1. 1.
    Argaç N.: On prime and semiprime rings with derivations. Algebra Colloquium 13, 371–380 (2006)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Beidar K.I., Martindale W.S. III, Mikhalev A.V.: Rings with Generalized Identities. Marcel Dekker, Inc., New York (1996)MATHGoogle Scholar
  3. 3.
    Brešar M.: The distance of the compositum of derivations to the generalized derivations. Glasgow Math. J. 33, 89–93 (1991)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Brešar M.: On generalized biderivations and related maps. J. Algebra 172, 764–786 (1995)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Brešar M., Martindale W.S. III, Miers C.R.: Centralizing maps in prime rings with involution. J. Algebra 161, 342–357 (1993)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Eremita D.: A functional identity with an automorphism in semiprime rings. Algebra Colloquium 8, 301–306 (2001)MATHMathSciNetGoogle Scholar
  7. 7.
    Fošner M., Vukman J.: Identities with generalized derivations in prime rings. Mediterranean J. Math. 9, 847–863 (2012)CrossRefMATHGoogle Scholar
  8. 8.
    Herstein I.N.: Rings with Involution. The University of Chicago Press, Chicago (1976)MATHGoogle Scholar
  9. 9.
    Hvala B.: Generalized derivations in rings. Comm. Algebra 26, 1147–1166 (1998)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Lanski C.: A note on GPIs and their coefficients. Proc. Am. Math. Soc. 98, 17–19 (1986)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Lee T.-K.: Generalized derivations of left faithful rings. Comm. Algebra 27, 4057–4073 (1999)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Lee T.-K.: Generalized skew derivations characterized by acting on zero products. Pac. J. Math. 216, 293–301 (2004)CrossRefMATHGoogle Scholar
  13. 13.
    Liu, K.-S.: Differential identities and constants of algebraic automorphisms in prime rings, Ph.D. Thesis, National Taiwan University, Taipei (2006)Google Scholar
  14. 14.
    Passman D.: Infinite Crossed Products. Academic Press, San Diego (1989)MATHGoogle Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Faculty of ManagementUniversity of PrimorskaKoperSlovenia

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