Research Article
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Year 2026, Volume: 55 Issue: 1 , 149 - 161 , 23.02.2026
https://doi.org/10.15672/hujms.1340737
https://izlik.org/JA77ZL25XG

Abstract

References

  • [1] M.N. Daif, When is a multiplicative derivation additive?, Int. J. Math. Math. Sci. 14 (3), 615-618, 1991.
  • [2] V. Darvish, M. Nouri, M. Razeghi and A. Taghavi, Nonlinear $*$-Jordan triple derivations on prime -algebras, Rocky Mountain J. Math. 50, 543-549, 2020.
  • [3] B.L.M. Ferreira, Additivity of elementary maps on alternative rings, Algebra Disc. Math. 28, 94-106, 2019.
  • [4] B.L.M. Ferreira and B.T. Costa, $*$-Jordan-type maps on $C^*$-algebras, Comm. Algebra 49, 5073-5082, 2021.
  • [5] J.C.M. Ferreira and B.L.M. Ferreira, Additivity of n-multiplicative maps on alternative rings, Comm. Algebra 44, 1557-1568, 2016.
  • [6] M. Ferrero and C. Haetinger, Higher derivations and a theorem by Herstein, Quaest. Math. 25 (2), 249-257, 2002.
  • [7] M. Ferrero and C. Haetinger, Higher derivations of semiprime rings, Comm. Algebra 30 (5), 2321-2333, 2002.
  • [8] A. Fošner, F. Wei and Z.K. Xiao, Nonlinear Lie-type derivations of von Neumann algebras and related topics, Colloq. Math. 132, 53-71, 2013.
  • [9] H. Hasse and F.K. Schmidt, Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper einer Unbestimmten (in German), J. Reine. Angew. Math. 177, 215-237, 1937.
  • [10] N. Heerema, Higher derivations and automorphisms of complete local rings, Bull. Amer. Math. Soc. 76, 1212-1225, 1970.
  • [11] D. Huo, B. Zheng and H. Liu, Nonlinear maps preserving Jordan triple $\eta-*$-products, J. Math. Anal. Appl. 430, 830-844, 2015.
  • [12] W. Jing, Nonlinear $*$-Lie derivations of standard operator algebras, Quaest. Math. 39, 1037-1046, 2016.
  • [13] A.N. Khan and H. Alhazmi, Multiplicative bi-skew Jordan triple derivations on prime $*$-algebra, Georgian Math. J. 30 (3), 389-396, 2023.
  • [14] L. Kong and J. Zhang, Nonlinear bi-skew Lie derivation on factor von Neumann algebras, Bull. Iranian Math. Soc. 47, 1097-1106, 2021.
  • [15] C. Li, Q. Chen and T. Wang, Nonlinear maps preserving the Jordan triple $*$-product on factors, Chinese Ann. Math. Ser. B 39, 633-642, 2018.
  • [16] C. Li, Y. Zhao and F. Zhao, Nonlinear $*$-Jordan-type derivations on $*$-algebras, Rocky Mountain J. Math. 51, 601-612, 2021.
  • [17] A. Nakajima, On generalized higher derivations, Turkish J. Math. 24 (3), 295-311, 2000.
  • [18] X.F. Qi and J.C. Hou, Lie higher derivations on nest algebras, Commun. Math. Res. 26 (2), 131-143, 2010.
  • [19] A. Roy and R. Sridharan, Higher derivations and central simple algebras, Nagoya Math. J. 32, 21-30, 1968.
  • [20] P. Šemrl, Additive derivations of some operator algebras, Illinois J. Math. 35, 234-240, 1991.
  • [21] A. Taghavi, H. Rohi and V. Darvish, Non-linear $*$-Jordan derivations on von Neumann algebras, Linear Multilinear Algebra 64, 426-439, 2016.
  • [22] F. Wei and Z.K. Xiao, Higher derivations of triangular algebras and its generalizations, Linear Algebra Appl. 435 (5), 1034-1054, 2011.
  • [23] Z.K. Xiao and F. Wei, Nonlinear Lie higher derivations on triangular algebras, Linear Multilinear Algebra 60 (8), 979-994, 2012.
  • [24] F.J. Zhang, X.F. Qi and J.H. Zhang, Nonlinear $*$-Lie higher derivations on factor von Neumann algebras, Bull. Iranian Math. Soc. 42 (3), 659-678, 2016.
  • [25] F. Zhao and C. Li, Nonlinear $*$-Jordan triple derivations on von Neumann algebras, Math. Slovaca 68, 163-170, 2018.

Non-linear bi-skew Jordan triple higher derivations on prime $*$-algebras

Year 2026, Volume: 55 Issue: 1 , 149 - 161 , 23.02.2026
https://doi.org/10.15672/hujms.1340737
https://izlik.org/JA77ZL25XG

Abstract

Let $\Delta =\{\mathcal{T}_n\}_{n\in \mathbb{N}}$ be a non-linear bi-skew Jordan triple higher derivation on a prime $*$-algebra $\mathfrak{A}$. In this article, we prove that $\Delta$ is an additive $*$-higher derivation on $\mathfrak{A}$.

References

  • [1] M.N. Daif, When is a multiplicative derivation additive?, Int. J. Math. Math. Sci. 14 (3), 615-618, 1991.
  • [2] V. Darvish, M. Nouri, M. Razeghi and A. Taghavi, Nonlinear $*$-Jordan triple derivations on prime -algebras, Rocky Mountain J. Math. 50, 543-549, 2020.
  • [3] B.L.M. Ferreira, Additivity of elementary maps on alternative rings, Algebra Disc. Math. 28, 94-106, 2019.
  • [4] B.L.M. Ferreira and B.T. Costa, $*$-Jordan-type maps on $C^*$-algebras, Comm. Algebra 49, 5073-5082, 2021.
  • [5] J.C.M. Ferreira and B.L.M. Ferreira, Additivity of n-multiplicative maps on alternative rings, Comm. Algebra 44, 1557-1568, 2016.
  • [6] M. Ferrero and C. Haetinger, Higher derivations and a theorem by Herstein, Quaest. Math. 25 (2), 249-257, 2002.
  • [7] M. Ferrero and C. Haetinger, Higher derivations of semiprime rings, Comm. Algebra 30 (5), 2321-2333, 2002.
  • [8] A. Fošner, F. Wei and Z.K. Xiao, Nonlinear Lie-type derivations of von Neumann algebras and related topics, Colloq. Math. 132, 53-71, 2013.
  • [9] H. Hasse and F.K. Schmidt, Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper einer Unbestimmten (in German), J. Reine. Angew. Math. 177, 215-237, 1937.
  • [10] N. Heerema, Higher derivations and automorphisms of complete local rings, Bull. Amer. Math. Soc. 76, 1212-1225, 1970.
  • [11] D. Huo, B. Zheng and H. Liu, Nonlinear maps preserving Jordan triple $\eta-*$-products, J. Math. Anal. Appl. 430, 830-844, 2015.
  • [12] W. Jing, Nonlinear $*$-Lie derivations of standard operator algebras, Quaest. Math. 39, 1037-1046, 2016.
  • [13] A.N. Khan and H. Alhazmi, Multiplicative bi-skew Jordan triple derivations on prime $*$-algebra, Georgian Math. J. 30 (3), 389-396, 2023.
  • [14] L. Kong and J. Zhang, Nonlinear bi-skew Lie derivation on factor von Neumann algebras, Bull. Iranian Math. Soc. 47, 1097-1106, 2021.
  • [15] C. Li, Q. Chen and T. Wang, Nonlinear maps preserving the Jordan triple $*$-product on factors, Chinese Ann. Math. Ser. B 39, 633-642, 2018.
  • [16] C. Li, Y. Zhao and F. Zhao, Nonlinear $*$-Jordan-type derivations on $*$-algebras, Rocky Mountain J. Math. 51, 601-612, 2021.
  • [17] A. Nakajima, On generalized higher derivations, Turkish J. Math. 24 (3), 295-311, 2000.
  • [18] X.F. Qi and J.C. Hou, Lie higher derivations on nest algebras, Commun. Math. Res. 26 (2), 131-143, 2010.
  • [19] A. Roy and R. Sridharan, Higher derivations and central simple algebras, Nagoya Math. J. 32, 21-30, 1968.
  • [20] P. Šemrl, Additive derivations of some operator algebras, Illinois J. Math. 35, 234-240, 1991.
  • [21] A. Taghavi, H. Rohi and V. Darvish, Non-linear $*$-Jordan derivations on von Neumann algebras, Linear Multilinear Algebra 64, 426-439, 2016.
  • [22] F. Wei and Z.K. Xiao, Higher derivations of triangular algebras and its generalizations, Linear Algebra Appl. 435 (5), 1034-1054, 2011.
  • [23] Z.K. Xiao and F. Wei, Nonlinear Lie higher derivations on triangular algebras, Linear Multilinear Algebra 60 (8), 979-994, 2012.
  • [24] F.J. Zhang, X.F. Qi and J.H. Zhang, Nonlinear $*$-Lie higher derivations on factor von Neumann algebras, Bull. Iranian Math. Soc. 42 (3), 659-678, 2016.
  • [25] F. Zhao and C. Li, Nonlinear $*$-Jordan triple derivations on von Neumann algebras, Math. Slovaca 68, 163-170, 2018.
There are 25 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Research Article
Authors

Asma Ali 0000-0001-7602-0268

Mohd Tasleem 0000-0002-2516-0612

Abdul Khan 0000-0002-5861-6137

Early Pub Date October 6, 2025
Publication Date February 23, 2026
DOI https://doi.org/10.15672/hujms.1340737
IZ https://izlik.org/JA77ZL25XG
Published in Issue Year 2026 Volume: 55 Issue: 1

Cite

APA Ali, A., Tasleem, M., & Khan, A. (2026). Non-linear bi-skew Jordan triple higher derivations on prime $*$-algebras. Hacettepe Journal of Mathematics and Statistics, 55(1), 149-161. https://doi.org/10.15672/hujms.1340737
AMA 1.Ali A, Tasleem M, Khan A. Non-linear bi-skew Jordan triple higher derivations on prime $*$-algebras. Hacettepe Journal of Mathematics and Statistics. 2026;55(1):149-161. doi:10.15672/hujms.1340737
Chicago Ali, Asma, Mohd Tasleem, and Abdul Khan. 2026. “Non-Linear Bi-Skew Jordan Triple Higher Derivations on Prime $*$-Algebras”. Hacettepe Journal of Mathematics and Statistics 55 (1): 149-61. https://doi.org/10.15672/hujms.1340737.
EndNote Ali A, Tasleem M, Khan A (February 1, 2026) Non-linear bi-skew Jordan triple higher derivations on prime $*$-algebras. Hacettepe Journal of Mathematics and Statistics 55 1 149–161.
IEEE [1]A. Ali, M. Tasleem, and A. Khan, “Non-linear bi-skew Jordan triple higher derivations on prime $*$-algebras”, Hacettepe Journal of Mathematics and Statistics, vol. 55, no. 1, pp. 149–161, Feb. 2026, doi: 10.15672/hujms.1340737.
ISNAD Ali, Asma - Tasleem, Mohd - Khan, Abdul. “Non-Linear Bi-Skew Jordan Triple Higher Derivations on Prime $*$-Algebras”. Hacettepe Journal of Mathematics and Statistics 55/1 (February 1, 2026): 149-161. https://doi.org/10.15672/hujms.1340737.
JAMA 1.Ali A, Tasleem M, Khan A. Non-linear bi-skew Jordan triple higher derivations on prime $*$-algebras. Hacettepe Journal of Mathematics and Statistics. 2026;55:149–161.
MLA Ali, Asma, et al. “Non-Linear Bi-Skew Jordan Triple Higher Derivations on Prime $*$-Algebras”. Hacettepe Journal of Mathematics and Statistics, vol. 55, no. 1, Feb. 2026, pp. 149-61, doi:10.15672/hujms.1340737.
Vancouver 1.Asma Ali, Mohd Tasleem, Abdul Khan. Non-linear bi-skew Jordan triple higher derivations on prime $*$-algebras. Hacettepe Journal of Mathematics and Statistics. 2026 Feb. 1;55(1):149-61. doi:10.15672/hujms.1340737