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Title: A Basis for Z-Graded Identities of Matrices over Infinite Fields
Authors: Azevedo, Sergio
Keywords: Matrix Algebra
Variety of Algebras
Polynomial Identities
Graded Identities
Issue Date: 2003
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 29, No 2, (2003), 149p-158p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 16R10, 16R20, 16R50
ISSN: 1310-6600
Appears in Collections:Volume 29 Number 2

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