International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 411-412
doi:10.1155/S016117129800057X
On a problem of commutativity of automorphims
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.
Abstract
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+α−1=β+β−1, then either α=β or α=β−1. As a consequence α and β commute and
in this situation the equation itself ensures the commutativity of α and β.