Abstract
Let R be a prime ring which is not commutative, with maximal symmetric ring of quotients Q ms (R), and let τ be an anti-automorphism of R. An additive map δ: R → Q ms (R) is called a Jordan τ-derivation if δ(x 2) = δ(x)x τ + xδ(x) for all x ∈ R. A Jordan τ-derivation of R is called X-inner if it is of the form x → ax τ − xa for x ∈ R, where a ∈ Q ms (R). It is proved that any Jordan τ-derivation of R is X-inner if either R is not a GPI-ring or R is a PI-ring except when charR = 2 and dim C RC = 4, where C is the extended centroid of R.
ACKNOWLEDGMENTS
The authors are grateful to the referee for carefully reading the manuscript.
Notes
Communicated by M. Bresar.