Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599303 | Linear Algebra and its Applications | 2014 | 15 Pages |
Abstract
Let R be a prime ring with center Z(R)Z(R) and with extended centroid C. We give a complete characterization of Jordan derivations of R when charR=2 and dimCRC=4dimCRC=4: An additive map δ:R→RCδ:R→RC is a Jordan derivation if and only if there exist a derivation d:R→RCd:R→RC and an additive map μ:R→Cμ:R→C such that δ=d+μδ=d+μ and μ(x2)=0μ(x2)=0 for all x∈Rx∈R. As consequences, it is proved among other things: Any Z(R)Z(R)-linear Jordan derivation of R is a derivation if dimCRC<∞dimCRC<∞. Moreover, if C is either a finite field or an algebraically closed field, where charC=2 and n≥2n≥2, then every Jordan derivation of Mn(C)Mn(C) is a derivation.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Tsiu-Kwen Lee, Jheng-Huei Lin,