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

Azevedo, 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 -