  We propose the ternary generalization of the classical anti-commutativity and
study the algebras whose generators are ternary anti-commutative. The integral
over an algebra with an arbitrary number of generators N is defined and the
formula of a change of variables is proved. In analogy with the fermion
integral we define an analogue of the Pfaffian for a cubic matrix by means of
Gaussian type integral and calculate its explicit form in the case of N=3.
