GENERALIZED JORDAN BI-DERIVATIONS ON TRIANGULAR ALGEBRA

Faiza Shujat; Aisha  Alsubhi; Abu Zaid Ansari

doi:10.5269/bspm.77333

Faiza Shujat Taibah University, Madinah KSA
Aisha Alsubhi Taibah University, Madinah KSA
Abu Zaid Ansari Department of Mathematics, Faculty of Science, Islamic University, KSA

Abstract

In the current investigation, our primary objective is to find the structure
of generalized Jordan biderivations on triangular algebra. Infact, we establish
that all generalized Jordan biderivations on a triangular algebra will be of the form
of an inner derivation. Our proof contains an entirely different approach and conclusion
from the existing classical theory [12] which states that if R is a prime ring
of characteristic different from 2, then any Jordan derivation of R is an ordinary
derivation.

Downloads

Download data is not yet available.

Author Biographies

Faiza Shujat, Taibah University, Madinah KSA

Associate Professor

Department of Mathematics

Aisha Alsubhi, Taibah University, Madinah KSA

Master Student

References

(1) Ahmad, W., Akhtar, M. S. and Mozumder, M., Characterization of (α, β)−
bi-derivations in triangular algebras, Ann. Univ. Ferrara., 70(2024), 1687–1696.
(2) Alsubhi, A., Shujat, F., and Fallatah, A., Bi-semiderivations on triangular
algebra, (2025) Preprint.
(3) Ansari, A. Z. and Shujat, F., Jordan ∗-derivations on standard operator
algebras Filomat, 37(1) (2023), 37–41.
(4) Benkoviˇc, D., Bi-derivations on triangular algebras, Linear Algebra Appl.,
431(9)(2009), 1587-1602.
(5) Bresar, M., Centralizing mappings and derivations in prime rings, J. Algebra,
156 (2) (1993), 385-394.
(6) Bresar, M. and Vukman, J., Jordan derivations on prime rings, Bull. Austral.
Math. Soc., 37(1988), 321-322.
(7) Cheung, W. S., Commuting maps of triangular algebras, J. London Math.
Soc., 63(1)(2001), 117–127.
(8) Cheung, W. S., Mappings on triangular algebras, PhD. Thesis, University of
Victoria, 2000.
(9) Cusack, J. M., Jordan Derivations on Rings, Proc. Amer. Math. Soc., 53(2)
(1975), 321-324.
(10) De Filippis, V., A product of two generalized derivations on polynomials in
prime rings, Collect. Math., 61(2010), 303–322.
(11) De Filippis, V., Tiwari, S. K. and Singh, S. K., Generalized g-derivations
on prime rings, Journal of Algebra and Its Applications, 22 (02) (2023),
235-247.
(12) Herstein, I. N., Jordan derivations of prime rings, Canad. Bull. Math., 43
(1957), 1104-1110.
(13) Lu, F. Y., Lie triple derivations on Nest algebras, Math. Nachr., 280(8)(2007),
882-887.
(14) Lu, F., The Jordan structure of CSL algebras, Studia Mathematica, 190(3)(2009),
283–299.
7
(15) Posner, E., Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957),
1093-1100.
(16) Qi, X. F. and Hou, J. C., Lie higher derivations on Nest algebras, Commun.
Math. Res., 26(2)(2010), 131-143.
(17) Zhang, J. H. and Yu, W.Y., Jordan derivations of triangular algebras, Linear
Algebra and its Applications, 419 (2006), 251–255.