Abstract
The aim of this article is to introduce the concept of centrally-extended Jordan epimorphisms and proving that if R is a non-commutative prime ring (∗-ring) of characteristic not two, and G is a CE-Jordan epimorphism such that [G(x), x] ∈ Z(R) ([G(x), x∗] ∈ Z(R)) for all x ∈ R, then R is an order in a central simple algebra of dimension at most 4 over its center or there is an element λ in the extended centroid of R such that G(x) = λx (G(x) = λx∗) for all x ∈ R.