Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME STUDIES ON JORDAN (𝛼, 1)* -BIDERIVATION IN RINGS WITH INVOLUTION

  • SK. HASEENA (Department of Mathematics, Sri Venkateswara University) ;
  • C. JAYA SUBBA REDDY (Department of Mathematics, Sri Venkateswara University)
  • Received : 2023.09.11
  • Accepted : 2024.01.16
  • Published : 2024.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

Let R be a ring with involution. In the present paper, we characterize biadditive mappings which satisfies some functional identities related to symmetric Jordan (𝛼, 1)*-biderivation of prime rings with involution. In particular, we prove that on a 2-torsion free prime ring with involution, every symmetric Jordan triple (𝛼, 1)*-biderivation is a symmetric Jordan (𝛼, 1)*-biderivation.

Keywords

Acknowledgement

The authors thanks the referee for their valuable suggestions towards the improvement of the paper.

References

  1. A. Shakir and A. Fosner, On Jordan (α, β)*-derivation in semiprime *-ring, Int. J. Algabra 2 (2010), 99-108.
  2. A. Shakir, A note on Jordan triple (α, β)*-derivation on H*-algebras, East-West J. Math. 13 (2011), 139-146.
  3. A. Shakir, M.S. Khan, On *-bimultipliers, Generalized *-biderivations and related mappings, Kyungpook Math. J. 51 (2011), 301-309. https://doi.org/10.5666/KMJ.2011.51.3.301
  4. A. Shakir, M. Fosner, A. Fosner, Khan, On generalized Jordan triple (α, β)*-derivations and related mappings, Medtirr. J. Math. 10 (2013), 1657-1668.
  5. A. Shakir, N.A. Dar, D. Pagon, On Jordan *-mappings in rings with involution, J. Egyptian Math. Soc. 24 (2016), 15-19. https://doi.org/10.1016/j.joems.2014.12.006
  6. M. Ashraf, A. Ali, S. Ali, On Lie ideals and generalized (θ, ϕ)-derivations in prime rings, Comm. Algebra 32 (2004), 2877-2785.
  7. M. Bresar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228. https://doi.org/10.1016/0021-8693(89)90285-8
  8. J.M. Cusack, Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324. https://doi.org/10.1090/S0002-9939-1975-0399182-5
  9. M. Fosner, D. Ilisevic, On Jordan triple derivations and related mappings, Mediterr. J. Math. 5 (2008), 415-427. https://doi.org/10.1007/s00009-008-0159-9
  10. I.N. Herstein, Topics in Ring Theory, Chicago Univ. Press, Chicago, 1969.
  11. C. Jaya Subba Reddy, Sk. Haseena, Homomorphism or Anti-Homomorphism of Left (α, 1) derivations in Prime rings, Int. J. Mathematical Archive 12 (2021), 45-49.
  12. C. Jaya Subba Reddy, Sk. Haseena, (α, 1)-Reverse derivations on Prime nearrings, Int. J. Algebra 15 (2021), 165-170. https://doi.org/10.12988/ija.2021.91561
  13. C. Jaya Subba Reddy, Sk. Haseena, and C. Divya, On Jordan ideals and Generalized (α, 1)-Reverse derivations in *-prime rings, Journal of University of Shanghai for Science and Technology 23 (2021), 236-242.
  14. C. Jaya Subba Reddy, Sk. Haseena, and C. Divya, Centralizing properties of (α, 1)-Reverse derivations in semiprime rings, Journal of Emerging Technologies and Innovative Research 8 (2021), 45-50.
  15. C. Jaya Subba Reddy, Sk. Haseena, Symmetric Generalized (α, 1)-Biderivations in Rings, The International Journal of Analytical and Experimental Modal analysis 14 (2022), 1944-1949.
  16. C. Jaya Subba Reddy, Sk. Haseena, Symmetric Generalized Reverse (α, 1)- Biderivations in Rings, JP Journal of Algebra, Number Theory and its applications 58 (2022), 37-43. https://doi.org/10.17654/0972555522033
  17. C.K. Liu and Q.K. Shiue, Generalized Jordan Triple (θ, π)-derivations of semiprime rings, Taiwanese J. Math. 11 (2007), 1397-1406.
  18. G. Maksa, Remark on symmetric bi-additive functions having non- negative diagonalization, Glas. Mat. Ser. III 15 (1980), 279-280.
  19. G. Maksa, On the trace of symmetric biderivations, C. R. Math. Rep. Acad. Sci. 9 (1987), 303-307.
  20. G. Naga Malleswari, S. Sreenivasulu, and G. Shobhalatha, Centralizing properties of (α, 1) derivations in Semiprime rings, Int. J. Math.& Appl. 8 (2020), 127-132.
  21. N. Rehman, M. Hongan and Al-Omary, Lie ideals and Jordan Triple derivations in rings, Rend. Sem. Mat. Univ. Padova 125 (2011), 147-156. https://doi.org/10.4171/rsmup/125-9
  22. N. Rehman and E. Koc, Lie ideals and Jordan Triple (α, β)-derivations in rings, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Sat. 69 (2020), 528-539.
  23. S. Ali, H. Alhazmi, and N.A. Khan, On Jordan (θ, ϕ)*- biderivation and in Rings with Involution, British J. Math.& Comp. Sci. 17 (2016), 1-7.
  24. J. Vukman, A note on Jordan *-derivations in semiprime rings with involution, Int. Math. Forum 13 (2006), 617-622. https://doi.org/10.12988/imf.2006.06053