On a certain identity satisfied by a derivation and an arbitrary additive mapping
The authors prove that if \(R\) is a prime ring with nonzero derivation \(D\) and additive mapping \(f\) so that \(D(x)f(x) = 0\) for all \(x \in R\), then there is a nonzero left ideal \(L\) of \(R\) and a nonzero right ideal \(T\) of \(R\) with \(f(L) = f(T) = 0\).
scientific article; zbMATH DE number 202384
scientific article