  We introduce Z_3-graded objects which are the generalization of the more
familiar Z_2-graded objects that are used in supersymmetric theories and in
many models of non-commutative geometry. First, we introduce the Z_3-graded
Grassmann algebra, and we use this object to construct the Z_3-matrices, which
are the generalizations of the supermatrices. Then, we generalize the concepts
of supertrace and superdeterminant.
