A special identity of \((\alpha,\beta)\)-derivations and its consequences
The paper deals with \((\alpha,\beta)\)-derivations of prime rings satisfying some special relations. In the main result \((\alpha,\beta)\)-derivations \(\delta,g,h\) satisfying \(\delta(x)=ag(x)+h(x)b\) for all \(x\) in a nonzero ideal \(U\) of a prime ring \(R\) are characterized. Here, \(a\) and \(b\) are noncentral elements of the symmetric Martindale ring of quotients of \(R\).
scientific article; zbMATH DE number 1054445