  In this paper, we study the class of Jordan dialgebras. We develop an
approach for reducing problems on dialgebras to the case of ordinary algebras.
It is shown that straightforward generalizations of the classical Cohn's,
Shirshov's, and Macdonald's Theorems do not hold for dialgebras. However, we
prove dialgebraic analogues of these statements. Also, we study polylinear
special identities which hold in all special Jordan algebras and do not hold in
all Jordan algebras. We find a natural correspondence between special
identities for ordinary algebras and dialgebras.
