Graded identities for the matrix algebra of order n over an infinite field

The algebra M,(K) of all square matrices of order n over a field K has a natural Z(n)-grading. In this paper, we generalize a result of Vasilovsky about the Z(n)-graded identities of the algebra M,(K). It is shown that, when K is an infinite field, all the Z(n)-graded polynomial identities of M-n(K) follow from the identities: x(1)x(2) = x(2)x(1), alpha(alpha1) = alpha(x(2)) = 0; x(1)x(3)x(2) = x(2)x(3)x(1), alpha(x(1)) = alpha(x(2)) = -alpha(x(3)); where alpha(x) is the degree of the indeterminate x.30125849586