GENERALIZED SKEW DERIVATIONS AS JORDAN HOMOMORPHISMS ON MULTILINEAR POLYNOMIALS

Vincenzo De Filippis
2015 Journal of the Korean Mathematical Society  
Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. Suppose that G is a nonzero generalized skew derivation of R, α is the associated automorphism of G, f (x 1 , . . . , xn) is a non-central multilinear polynomial over C with n non-commuting variables and S = {f (r 1 , . . . , rn) | r 1 , . . . , rn ∈ R}. If G acts as a Jordan homomorphism on S, then either G(x) = x for all x ∈ R, or G = α.
doi:10.4134/jkms.2015.52.1.191 fatcat:duk7arkptnh23dep2y7oihc7vi