GRADED IDENTITIES FOR THE MATRIX ALGEBRA OF ORDER OVER AN INFINITE FIELD

ABSTRACT

The algebra of all square matrices of order over a field has a natural -grading. In this paper, we generalize a result of Vasilovsky about the -graded identities of the algebra . It is shown that, when is an infinite field, all the -graded polynomial identities of follow from the identities:

where is the degree of the indeterminate .

ACKNOWLEDGMENTS

I would like to thank Plamen Koshlukov for suggesting the problem, and for useful discussions and advices. Thanks are due to the referee whose valuable remarks improved the exposition.

Supported by PhD scholarship from FAPESP, Grant No. 98/16445-5.