Generalized Jordan triple (ζ, ξ)-derivations on semiprime rings

Document Type : Special Issue: First Joint IIIMT-Algebra Forum Conference 2023

Authors

1 Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, K.S.A.

2 Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India

Abstract

The purpose of this research is to demonstrate the following assertions: an additive mapping H is a generalized (ζ,ξ)-derivation associated with a (ζ,ξ)-derivation h, where ζ,ξ are endomorphisms on a (m+n+p1)!-torsion free semiprime ring A. Here we prove another result in the setting of the generalized left (ζ,ξ)-derivation on A.

Keywords

Main Subjects


[1] Albas, E. (2007). On -centralizers of semiprime rings. Siberian Math. J. 48(2), 191-196.
[2] Ali, S. (2011). On generalized left derivations in rings and Banach algebras. Aequat., Math. 81, 209-226.
[3] Ali, S. & Haetinger, C. (2008). Jordan -centralizer in rings and some applications. Bol. Soc. Paran. Mat. 26, no. 1-2, 71-80.
[4] Bresar, M. (1989). Jordan mappings of semiprime rings. J. Algebra, 17, 218-228.
[5] Cusack, J. M. (1975). Jordan derivations in rings. Proc. Amer. Math. Soc. 53(2), 321-324.
[6] Herstein, I. N. (1957). Derivations in prime rings. Proc. Amer. Math. Soc. 8, 1104-1110.
[7] Jing, W. & Lu, S. (2003). Generalized Jordan derivations on prime rings and standard operator algebras. Taiwanese Journal of Mathematics, 7(4), 605-613.
[8] Lanski, C. (2007). Generalized derivations and n-th power maps in rings. Comm. Algebra 35, no. 11, 3660-3672.
[9] Liu, C. K. & Shiue, Q. K. (2007). Generalized Jordan triple (; &)-derivations of semiprime rings. Taiwanese J. Math. 11, 1397-1406.
Volume 13, Issue 5 - Serial Number 30
Special Issue: First Joint IIIMT-Algebra Forum Conference 2023
December 2024
Pages 41-49
  • Receive Date: 02 May 2024
  • Revise Date: 04 November 2024
  • Accept Date: 22 November 2024