International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 411-412

On a problem of commutativity of automorphims

M. Anwar Chaudhry and A. B. Thaheem

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 8 January 1996

Copyright © 1998 M. Anwar Chaudhry and A. B. Thaheem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this note we provide a partial answer to a problem proposed by M. Brehr. We prove that if α,β are automorphisms of a commutative prime ring of characteristic not equal to 2 satisfying the equation α+α1=β+β1, then either α=β or α=β1. As a consequence α and β commute and in this situation the equation itself ensures the commutativity of α and β.