Jordan elementary maps on rings Original Research Article

Let image be a 2-torsion free prime ring containing a non-trivial idempotent and image be an arbitrary ring. Suppose that image and image are surjective maps such thatimagefor all image, image. Then both M and M* are additive. In particular, a bijective map image satisfying φ(xyx)=φ(x)φ(y)φ(x) for all image is additive.