On a problem of commutativity of automorphims

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.

Keywords

• Prime ring
• automorphism.