SPECIAL AND EXCEPTIONAL JORDAN DIALGEBRAS.

In this paper, we study the class of Jordan dialgebras (also called quasi-Jordan algebras). 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 multilinear 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. [ABSTRACT FROM AUTHOR]