Let A be an arbitrary -algebra with unit I over the real or complex eld F that contains a nontrivial idempotent P1 and n 1 a natural number. Assume that ' : A ! A be a surjective map on A such that ' satis es condition '(P) n1 '(P) '(A) = P n1 P A, for every A 2 A and projection P 2 fP1; I P1g, where A n1 A with repeat n 1 times A is the Jordan multiple -product. Then '(A) = '(I)A for all A 2 A and '(I)2 = I.
