Research Article
BibTex RIS Cite

CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS

Year 2021, Volume: 29 Issue: 29, 50 - 62, 05.01.2021
https://doi.org/10.24330/ieja.852003

Abstract

The purpose of the present paper is to classify generalized derivations satisfying more specific algebraic identities in a prime ring with
involution of the second kind. Some well-known results
characterizing commutativity of prime rings by derivations have
been generalized by using generalized derivation.

References

  • S. Ali and N. A. Dar, On *-centralizing mapping in rings with involution, Georgian Math. J., 21(1) (2014), 25-28.
  • S. Ali, N. A. Dar and M. Asci, On derivations and commutativity of prime rings with involution, Georgian Math. J., 23(1) (2016), 9-14.
  • M. Ashraf, N. Rehman, S. Ali and M. R. Mozumder, On semiprime rings with generalized derivations, Bol. Soc. Parana. Mat., (3), 28(2) (2010), 25-32.
  • M. Bresar, Semiderivations of prime rings, Proc. Amer. Math. Soc., 108(4) (1990), 859-860.
  • M. Bresar, On generalized biderivations and related maps, J. Algebra, 172(3) (1995), 764-786.
  • V. De Filippis, N. Rehman and A. Ansari, Lie ideals and generalized deriva- tions in semiprime rings, Iran. J. Math. Sci. Inform., 10(2) (2015), 45-54.
  • B. Hvala, Generalized derivations in rings, Comm. Algebra, 26 (1998), 1147- 1166.
  • M. A. Idrissi and L. Oukhtite, Some commutativity theorems for rings with involution involving generalized derivations, Asian-Eur. J. Math., 12(1) (2019), 1950001 (11 pp).
  • C. Lanski, Differential identities, Lie ideals and Posner's theorems, Pacific J. Math., 134(2) (1988), 275-297.
  • M. R. Khan and M. M. Hasnain, On semiprime rings with generalized derivations, Kyungpook Math. J., 53(4) (2013), 565-571.
  • T. K. Lee, Generalized derivations of left faithful rings, Comm. Algebra, 27 (1999), 4057-4073.
  • B. Nejjar, A. Kacha, A. Mamouni and L. Oukhtite, Certain commutativity criteria for rings with involution involving generalized derivations, Georgian Math. J., 27(1) (2020), 133-139.
  • L. Oukhtite and A. Mamouni, Generalized derivations centralizing on Jordan ideals of rings with involution, Turkish J. Math., 38(2) (2014), 225-232.
  • E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
Year 2021, Volume: 29 Issue: 29, 50 - 62, 05.01.2021
https://doi.org/10.24330/ieja.852003

Abstract

References

  • S. Ali and N. A. Dar, On *-centralizing mapping in rings with involution, Georgian Math. J., 21(1) (2014), 25-28.
  • S. Ali, N. A. Dar and M. Asci, On derivations and commutativity of prime rings with involution, Georgian Math. J., 23(1) (2016), 9-14.
  • M. Ashraf, N. Rehman, S. Ali and M. R. Mozumder, On semiprime rings with generalized derivations, Bol. Soc. Parana. Mat., (3), 28(2) (2010), 25-32.
  • M. Bresar, Semiderivations of prime rings, Proc. Amer. Math. Soc., 108(4) (1990), 859-860.
  • M. Bresar, On generalized biderivations and related maps, J. Algebra, 172(3) (1995), 764-786.
  • V. De Filippis, N. Rehman and A. Ansari, Lie ideals and generalized deriva- tions in semiprime rings, Iran. J. Math. Sci. Inform., 10(2) (2015), 45-54.
  • B. Hvala, Generalized derivations in rings, Comm. Algebra, 26 (1998), 1147- 1166.
  • M. A. Idrissi and L. Oukhtite, Some commutativity theorems for rings with involution involving generalized derivations, Asian-Eur. J. Math., 12(1) (2019), 1950001 (11 pp).
  • C. Lanski, Differential identities, Lie ideals and Posner's theorems, Pacific J. Math., 134(2) (1988), 275-297.
  • M. R. Khan and M. M. Hasnain, On semiprime rings with generalized derivations, Kyungpook Math. J., 53(4) (2013), 565-571.
  • T. K. Lee, Generalized derivations of left faithful rings, Comm. Algebra, 27 (1999), 4057-4073.
  • B. Nejjar, A. Kacha, A. Mamouni and L. Oukhtite, Certain commutativity criteria for rings with involution involving generalized derivations, Georgian Math. J., 27(1) (2020), 133-139.
  • L. Oukhtite and A. Mamouni, Generalized derivations centralizing on Jordan ideals of rings with involution, Turkish J. Math., 38(2) (2014), 225-232.
  • E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

M. A. Idrıssı This is me

L. Oukhtıte This is me

Publication Date January 5, 2021
Published in Issue Year 2021 Volume: 29 Issue: 29

Cite

APA Idrıssı, M. A., & Oukhtıte, L. (2021). CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS. International Electronic Journal of Algebra, 29(29), 50-62. https://doi.org/10.24330/ieja.852003
AMA Idrıssı MA, Oukhtıte L. CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS. IEJA. January 2021;29(29):50-62. doi:10.24330/ieja.852003
Chicago Idrıssı, M. A., and L. Oukhtıte. “CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS”. International Electronic Journal of Algebra 29, no. 29 (January 2021): 50-62. https://doi.org/10.24330/ieja.852003.
EndNote Idrıssı MA, Oukhtıte L (January 1, 2021) CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS. International Electronic Journal of Algebra 29 29 50–62.
IEEE M. A. Idrıssı and L. Oukhtıte, “CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS”, IEJA, vol. 29, no. 29, pp. 50–62, 2021, doi: 10.24330/ieja.852003.
ISNAD Idrıssı, M. A. - Oukhtıte, L. “CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS”. International Electronic Journal of Algebra 29/29 (January 2021), 50-62. https://doi.org/10.24330/ieja.852003.
JAMA Idrıssı MA, Oukhtıte L. CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS. IEJA. 2021;29:50–62.
MLA Idrıssı, M. A. and L. Oukhtıte. “CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS”. International Electronic Journal of Algebra, vol. 29, no. 29, 2021, pp. 50-62, doi:10.24330/ieja.852003.
Vancouver Idrıssı MA, Oukhtıte L. CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS. IEJA. 2021;29(29):50-62.