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Authors:	Sergei Yu. Vasilovsky

Affiliation:	Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni, Swaziland, Southern Africa - Institute of Mathematics, Novosibirsk 630090, Russia

Abstract:	The algebra of all matrices over a field has a natural $mathbf{Z}_n$ -grading $M_n(F)=sum _{alphain mathbf{Z}_n}bigoplusmathcal{M}_n^{(alpha )}$ . In this paper graded identities of the $mathbf{Z}_n$ -graded algebra over a field of characteristic zero are studied. It is shown that all the $mathbf{Z}_n$ -graded polynomial identities of follow from the following: $begin{displaymath}x_1x_2-x_2x_1=0,~~~~alpha (x_1)=alpha (x_2)=overline{0};end{displaymath}$ $begin{displaymath}x_1xx_2-x_2xx_1=0,~~~~alpha (x_1)=alpha (x_2)=-alpha (x).end{displaymath}$

Keywords:	Graded polynomial identities full matrix algebra

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