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Lee, Tsiu-Kwen; Lin, Jheng-Huei
Linear algebra and its applications, 12/2014, Letnik: 462Journal Article
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 dimCRC=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 dimCRC<∞. 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.
