Jordan \(\sigma\)-derivations of prime rings
In this paper, a complete characterization is given for Jordan \(\sigma\)-derivations of a prime ring \(R\) with \(\sigma\) an epimorphism. Such a Jordan \(\sigma\)-derivation \(\delta:R\rightarrow Q_{mr}(R)\) is either a \(\sigma\)-derivation or \(\delta(x)=ud(x)+\mu(x)u\) for all \(x\in R\) for some derivation \(d:R\rightarrow Q_{mr}(R)\), unit \(u\in Q_{mr}(R)\), and additive map \(\mu:R\rightarrow C\) satisfying \(\mu(x^{2})=0\) for all \(x\in R\). In case that \(\sigma\) is an X-outer automorphism, \(\delta\) is always a \(\sigma\)-derivation. A major part of the proof is to handle the case where \(R\) is a prime GPI-ring but is not a PI-ring, and the tool is built using the theory of functional identities.
scientific article; zbMATH DE number 6715759