On Lie ideals and $ (\sigma, \tau) $-Jordan derivations on prime rings

Authors

  • M. Ashraf
  • M. A. Quadri
  • Nadeem-Ur-Rehman

DOI:

https://doi.org/10.5556/j.tkjm.32.2001.338

Abstract

Let $ R $ be a prime ring with characteristic different from two and let $ U $ be a Lie ideal of $ R $ such that $ u^2 \in U $ for all $ u \in U $. Suppose that $ \sigma, \tau $ are automorphisms of $ R $. In the present paper, it is shown that if $ d $ is an additive mapping of $ R $ into itself satisfying $ d (u^2) = d(u) \sigma (v) + \tau (u) d(v) $ for all $ u,v \in U $, then $ d(uv) = d(u) \sigma (v) + \tau(u) d(v) $ for all $ u, v \in U $.

Author Biographies

M. Ashraf

Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. Box. 80203, Jeddah 21589, Saudi-Arabia.

M. A. Quadri

Department of Mathematics, Aligarh Muslim University, Aligarh, India.

Published

2001-12-31

How to Cite

Ashraf, M., Quadri, M. A., & Nadeem-Ur-Rehman. (2001). On Lie ideals and $ (\sigma, \tau) $-Jordan derivations on prime rings. Tamkang Journal of Mathematics, 32(4), 247–252. https://doi.org/10.5556/j.tkjm.32.2001.338

Issue

Section

Papers