SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2020 / Cilt: 69 - Sayı: 1

Lie ideals and Jordan triple (α,β)-derivations in rings

Emine KOÇ SÖGÜTCÜ
Nadeem ur Rehman
Pages
528–539
Publication Date
2020-06-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple (α,β)-derivation (resp. generalized Jordan triple (α,β)-derivation) on Lie ideal L is an (α,β)-derivation on L (resp. generalized (α,β)-derivation on L)

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple (α,β)-derivation (resp. generalized Jordan triple (α,β)-derivation) on Lie ideal L is an (α,β)-derivation on L (resp. generalized (α,β)-derivation on L)
📊
Key Findings & Data:In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple (α,β)-derivation (resp. generalized Jordan triple (α,β)-derivation) on Lie ideal L is an (α,β)-derivation on L (resp. generalized (α,β)-derivation on L)
💡
Conclusion & Impact:In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple (α,β)-derivation (resp. generalized Jordan triple (α,β)-derivation) on Lie ideal L is an (α,β)-derivation on L (resp. generalized (α,β)-derivation on L)
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Semiprime Rings · Lie ideals · Jordan triple (α.β)-derivations

Abstract

In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple (α,β)-derivation (resp. generalized Jordan triple (α,β)-derivation) on Lie ideal L is an (α,β)-derivation on L (resp. generalized (α,β)-derivation on L)

🔖

Cite This Article

SÖGÜTCÜ, E. K., Rehman, N. U. (2020). Lie ideals and Jordan triple (α,β)-derivations in rings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 69 - Sayı: 1, 528–539. https://ajindex.com/articles/746854

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (22)

  1. Ashraf, M., Ali, A. and Ali, Shakir, On Lie ideals and generalized (θ,φ)-derivations in prime rings, Comm. Algebra, 32, (2004), 2877-2785.
  2. Ashraf, M., Rehman, N. and Ali, Shakir, On Lie ideals and Jordan generalized derivations of prime rings, Indian J. Pure and Appl. math., 32(2), (2003), 291-294.
  3. Ashraf, M. and Rehman, N., On Jordan generalized derivations in rings, Math. J. Okayama Univ., 42, (2000), 7-9.
  4. J. Bergen, I. N. Herstein, and J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71, (1981), 259-267.
  5. Bresar, M., On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J., 33(1), (1991), 89-93.
  6. Bresar, M., Jordan mappings of semiprime rings, J. Algebra, 127, (1989), 218-228.
  7. Bresar, M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc., 104, (1988), 1003-1006.
  8. Bresar, M. and Vukman, J., Jordan derivations on prime rings, Bull. Austral. Math. Soc., 37, (1988), 321-322.
  9. Chuang, C, GPI's having coefficients in Utumi Quotient rings, Proc. Amer. Math. Soc., 103 (1988), 723-728.
  10. Cusack, J. M., Jordan derivations on rings, Proc. Amer. Math. Soc., 53, (1975), 321-324.
  11. Herstein, I. N., Topics in Ring Theory, Chicago Univ. Press, Chicago, 1969.
  12. Hongan, M., Rehman, N., Radwan, M. Lie ideals and Joudan Triple Derivations in rings, Rend. Sem. Mat. Univ. Padova, 125, (2011).
  13. Hvala, B., Generalized derivations in rings, Comm. Algebra, 26(1998), 1149-1166.
  14. Jing, W. and Lu, S., Generalized Jordan derivations on prime rings and standard operator algebras, Taiwanese J. Math., 7, (2003), 605-613.
  15. Liu, C. K. and Shiue, Q.K., Generalized Jordan triple (θ,φ)-derivations of semiprime rings, Taiwanese J. Math., 11, (2007), 1397-1406.
  16. Lanski, C., Generalized derivations and nth power maps in rings, Comm. Algebra, 35, (2007), 3660-3672.
  17. Martindale III, W. S., Prime ring satisfying a generalized polynomial identity, J. Algebra, 12, (1969), 576-584.
  18. Molnar, L., On centralizers of an H^{∗}-algebra, Publ. Math. Debrecen, 46, 1-2, (1995), 89-95, (2003), 277-283.
  19. Rehman, N. and Hongan, M., Generalized Jordan derivations on Lie ideals associate with Hochschild 2-cocycles of rings, Rend. Circ. Mat. Palermo, (2) 60, No. 3, (2011), 437-444.
  20. Vukman, J., A note on generalized derivations of semiprime rings, Taiwanese J. Math., 11, (2007), 367-370.
  21. Vukman, J. and Kosi-Ulbl, Irena, On centralizers of semiprime rings, Aequationes Math., 66, (2003), 277-283.
  22. Vukman, J., Centralizers of semiprime rings, Comment. Math.