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

Year 2020, Volume: 69 Issue: 1, 528 - 539, 30.06.2020
https://doi.org/10.31801/cfsuasmas.549472

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)

References

  • Ashraf, M., Ali, A. and Ali, Shakir, On Lie ideals and generalized (θ,φ)-derivations in prime rings, Comm. Algebra, 32, (2004), 2877-2785.
  • 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.
  • Ashraf, M. and Rehman, N., On Jordan generalized derivations in rings, Math. J. Okayama Univ., 42, (2000), 7-9.
  • J. Bergen, I. N. Herstein, and J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71, (1981), 259-267.
  • Bresar, M., On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J., 33(1), (1991), 89-93.
  • Bresar, M., Jordan mappings of semiprime rings, J. Algebra, 127, (1989), 218-228.
  • Bresar, M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc., 104, (1988), 1003-1006.
  • Bresar, M. and Vukman, J., Jordan derivations on prime rings, Bull. Austral. Math. Soc., 37, (1988), 321-322.
  • Chuang, C, GPI's having coefficients in Utumi Quotient rings, Proc. Amer. Math. Soc., 103 (1988), 723-728.
  • Cusack, J. M., Jordan derivations on rings, Proc. Amer. Math. Soc., 53, (1975), 321-324.
  • Herstein, I. N., Topics in Ring Theory, Chicago Univ. Press, Chicago, 1969.
  • Hongan, M., Rehman, N., Radwan, M. Lie ideals and Joudan Triple Derivations in rings, Rend. Sem. Mat. Univ. Padova, 125, (2011).
  • Hvala, B., Generalized derivations in rings, Comm. Algebra, 26(1998), 1149-1166.
  • Jing, W. and Lu, S., Generalized Jordan derivations on prime rings and standard operator algebras, Taiwanese J. Math., 7, (2003), 605-613.
  • Liu, C. K. and Shiue, Q.K., Generalized Jordan triple (θ,φ)-derivations of semiprime rings, Taiwanese J. Math., 11, (2007), 1397-1406.
  • Lanski, C. , Generalized derivations and nth power maps in rings, Comm. Algebra, 35, (2007), 3660-3672.
  • Martindale III, W. S., Prime ring satisfying a generalized polynomial identity, J. Algebra, 12, (1969), 576-584.
  • Molnar, L. , On centralizers of an H^{∗}-algebra, Publ. Math. Debrecen, 46, 1-2, (1995), 89-95, (2003), 277-283.
  • 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.
  • Vukman, J., A note on generalized derivations of semiprime rings, Taiwanese J. Math., 11, (2007), 367-370.
  • Vukman, J. and Kosi-Ulbl, Irena, On centralizers of semiprime rings, Aequationes Math., 66, (2003), 277-283.
  • Vukman, J., Centralizers of semiprime rings, Comment. Math. Univ. Carol., 42(2), (2001), 237-245.
  • Vukman, J., An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolinae, 40(3), (1999), 447-456, 2, (2001), 237-245.
  • Zalar, B., On centralizers of semiprime rings, Comment. Math. Univ. Carolinae, 32, (1991), 609-614.
Year 2020, Volume: 69 Issue: 1, 528 - 539, 30.06.2020
https://doi.org/10.31801/cfsuasmas.549472

Abstract

References

  • Ashraf, M., Ali, A. and Ali, Shakir, On Lie ideals and generalized (θ,φ)-derivations in prime rings, Comm. Algebra, 32, (2004), 2877-2785.
  • 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.
  • Ashraf, M. and Rehman, N., On Jordan generalized derivations in rings, Math. J. Okayama Univ., 42, (2000), 7-9.
  • J. Bergen, I. N. Herstein, and J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71, (1981), 259-267.
  • Bresar, M., On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J., 33(1), (1991), 89-93.
  • Bresar, M., Jordan mappings of semiprime rings, J. Algebra, 127, (1989), 218-228.
  • Bresar, M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc., 104, (1988), 1003-1006.
  • Bresar, M. and Vukman, J., Jordan derivations on prime rings, Bull. Austral. Math. Soc., 37, (1988), 321-322.
  • Chuang, C, GPI's having coefficients in Utumi Quotient rings, Proc. Amer. Math. Soc., 103 (1988), 723-728.
  • Cusack, J. M., Jordan derivations on rings, Proc. Amer. Math. Soc., 53, (1975), 321-324.
  • Herstein, I. N., Topics in Ring Theory, Chicago Univ. Press, Chicago, 1969.
  • Hongan, M., Rehman, N., Radwan, M. Lie ideals and Joudan Triple Derivations in rings, Rend. Sem. Mat. Univ. Padova, 125, (2011).
  • Hvala, B., Generalized derivations in rings, Comm. Algebra, 26(1998), 1149-1166.
  • Jing, W. and Lu, S., Generalized Jordan derivations on prime rings and standard operator algebras, Taiwanese J. Math., 7, (2003), 605-613.
  • Liu, C. K. and Shiue, Q.K., Generalized Jordan triple (θ,φ)-derivations of semiprime rings, Taiwanese J. Math., 11, (2007), 1397-1406.
  • Lanski, C. , Generalized derivations and nth power maps in rings, Comm. Algebra, 35, (2007), 3660-3672.
  • Martindale III, W. S., Prime ring satisfying a generalized polynomial identity, J. Algebra, 12, (1969), 576-584.
  • Molnar, L. , On centralizers of an H^{∗}-algebra, Publ. Math. Debrecen, 46, 1-2, (1995), 89-95, (2003), 277-283.
  • 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.
  • Vukman, J., A note on generalized derivations of semiprime rings, Taiwanese J. Math., 11, (2007), 367-370.
  • Vukman, J. and Kosi-Ulbl, Irena, On centralizers of semiprime rings, Aequationes Math., 66, (2003), 277-283.
  • Vukman, J., Centralizers of semiprime rings, Comment. Math. Univ. Carol., 42(2), (2001), 237-245.
  • Vukman, J., An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolinae, 40(3), (1999), 447-456, 2, (2001), 237-245.
  • Zalar, B., On centralizers of semiprime rings, Comment. Math. Univ. Carolinae, 32, (1991), 609-614.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Emine Koç Sögütcü 0000-0002-8328-4293

Nadeem ur Rehman 0000-0003-3955-7941

Publication Date June 30, 2020
Submission Date April 4, 2019
Acceptance Date October 5, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Koç Sögütcü, E., & 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, 69(1), 528-539. https://doi.org/10.31801/cfsuasmas.549472
AMA Koç Sögütcü E, Rehman Nu. Lie ideals and Jordan triple (α,β)-derivations in rings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):528-539. doi:10.31801/cfsuasmas.549472
Chicago Koç Sögütcü, Emine, and Nadeem ur Rehman. “Lie Ideals and Jordan Triple (α,β)-Derivations in Rings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 528-39. https://doi.org/10.31801/cfsuasmas.549472.
EndNote Koç Sögütcü E, Rehman Nu (June 1, 2020) Lie ideals and Jordan triple (α,β)-derivations in rings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 528–539.
IEEE E. Koç Sögütcü and N. u. Rehman, “Lie ideals and Jordan triple (α,β)-derivations in rings”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 528–539, 2020, doi: 10.31801/cfsuasmas.549472.
ISNAD Koç Sögütcü, Emine - Rehman, Nadeem ur. “Lie Ideals and Jordan Triple (α,β)-Derivations in Rings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 528-539. https://doi.org/10.31801/cfsuasmas.549472.
JAMA Koç Sögütcü E, Rehman Nu. Lie ideals and Jordan triple (α,β)-derivations in rings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:528–539.
MLA Koç Sögütcü, Emine and Nadeem ur Rehman. “Lie Ideals and Jordan Triple (α,β)-Derivations in Rings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 528-39, doi:10.31801/cfsuasmas.549472.
Vancouver Koç Sögütcü E, Rehman Nu. Lie ideals and Jordan triple (α,β)-derivations in rings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):528-39.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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