A note on commutativity of automorphisms (Q1380980)

The authors continue the series of papers on ring automorphisms \(\alpha\), \(\beta\) satisfying \(\alpha+\alpha^{-1}=\beta+\beta^{-1}\). Actually, in the paper under review, they consider a somewhat more general identity \(\alpha+m\alpha^{-1}=\beta+m\beta^{-1}\) where \(m\) is an integer. A certain condition implying the commutativity of \(\alpha\) and \(\beta\) is established.