Geodesic
A Basis for Z-Graded Identities of Matrices over Infinite Fields
Serdica Mathematical Journal, Tome 29 (2003) no. 2, pp. 149-158.

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The algebra Mn(K) of the matrices n × n over a field K can be regarded as a Z-graded algebra. In this paper, it is proved that if K is an infinite field, all the Z-graded polynomial identities of Mn(K) follow from the identities: x = 0, |α(x)| ≥ n, xy = yx, α(x) = α(y) = 0, xyz = zyx, α(x) = −α(y) = α(z ), where α is the degree of the corresponding variable. This is a generalization of a result of Vasilovsky about the Z-graded identities of the algebra Mn(K) over fields of characteristic 0.
Keywords: Matrix Algebra, Variety of Algebras, Polynomial Identities, Graded Identities 
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Azevedo, Sergio. A Basis for Z-Graded Identities of Matrices over Infinite Fields. Serdica Mathematical Journal, Tome 29 (2003) no. 2, pp. 149-158. http://geodesic.mathdoc.fr/item/SMJ2_2003_29_2_a3/