Jordan derivations of prime rings with characteristic two

Abstract

Let R be a prime ring with center Z(R) and with extended centroid C. We give a complete characterization of Jordan derivations of R when charR=2 and dimC⁡RC=4: An additive map δ:R→RC is a Jordan derivation if and only if there exist a derivation d:R→RC and an additive map μ:R→C such that δ=d+μ and μ(x2)=0 for all x∈R. As consequences, it is proved among other things: Any Z(R)-linear Jordan derivation of R is a derivation if dimC⁡RC<∞. Moreover, if C is either a finite field or an algebraically closed field, where charC=2 and n≥2, then every Jordan derivation of Mn(C) is a derivation.