# A Basis for Z-Graded Identities of Matrices over Infinite Fields

Serdica Mathematical Journal (2003)

- Volume: 29, Issue: 2, page 149-158
- ISSN: 1310-6600

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topAzevedo, Sergio. "A Basis for Z-Graded Identities of Matrices over Infinite Fields." Serdica Mathematical Journal 29.2 (2003): 149-158. <http://eudml.org/doc/219660>.

@article{Azevedo2003,

abstract = {2000 Mathematics Subject Classification: 16R10, 16R20, 16R50The 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.Supported by postdoctoral grant from FAPESP, No. 02/11776-5},

author = {Azevedo, Sergio},

journal = {Serdica Mathematical Journal},

keywords = {Matrix Algebra; Variety of Algebras; Polynomial Identities; Graded Identities; algebras with polynomial identities; graded identities; varieties of algebras; matrix algebras; bases of identities},

language = {eng},

number = {2},

pages = {149-158},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {A Basis for Z-Graded Identities of Matrices over Infinite Fields},

url = {http://eudml.org/doc/219660},

volume = {29},

year = {2003},

}

TY - JOUR

AU - Azevedo, Sergio

TI - A Basis for Z-Graded Identities of Matrices over Infinite Fields

JO - Serdica Mathematical Journal

PY - 2003

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 29

IS - 2

SP - 149

EP - 158

AB - 2000 Mathematics Subject Classification: 16R10, 16R20, 16R50The 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.Supported by postdoctoral grant from FAPESP, No. 02/11776-5

LA - eng

KW - Matrix Algebra; Variety of Algebras; Polynomial Identities; Graded Identities; algebras with polynomial identities; graded identities; varieties of algebras; matrix algebras; bases of identities

UR - http://eudml.org/doc/219660

ER -

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