Jordan derivations of prime rings with characteristic two
Journal
Linear Algebra and Its Applications
Journal Volume
462
Pages
1-15
Date Issued
2014
Author(s)
Lin, J.-H.
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 xεR. 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 ≥2, then every Jordan derivation of Mn(C) is a derivation. © 2014 Elsevier Inc.
Type
journal article