Let A be an arbitrary C-algebra which contains a nontrivial projection P1 and let ' V A ! A be a surjective map which satisfies '.A1/ '.A2/ '.An1/ '.P/ D A1 A2 An1 P for every A1; A2; : : : ; An1 2 A .n 3/, P 2 fP1; I P1g, and some 2 C; such that jj D 1, 6D 1, and A1 A2 An1 P is the Jordan multiple --product where A1 A2 D A1A2 CA2A 1 : We determine the concrete form of map ' on any arbitrary C-algebra. Also, if n > 3, D 1 and A is an arbitrary -algebra (with unit I ), over the complex field C which contains a nontrivial projection P1, then ' is of the form '.T / D T '.I / for all T 2 A.
