ON LIE IDEALS AND LEFT JORDAN σ-CENTRALIZERS OF 2-TORSION-FREE RINGS

B. Zalar proved that any left (resp. right) Jordan centralizer on a 2-torsion-free semiprime ring is a left (resp. right) centralizer. We prove this question changing the semiprimality condition on R. The main result of this paper is the following. Let R be a 2-torsionfree ring which has a commutator right (resp. left) nonzero divisor and let G: R → R be left (resp. right) Jordan σ-centralizer mapping of , where σ is an automorphism of R. Then G is a left (resp. right) -centralizer mapping of R.