FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 3, PAGES 193-203

Standard basis in the $T$-ideal formed by polynomial identities of triangular matrices

V. N. Latyshev

Abstract

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We give the definition of a standard basis of a $T$-ideal of the free associative algebra over a field of zero characteristic and indicate some basis called canonical in the linear space of $n$-linear forms. Using this basis, we construct a standard basis in the $T$-ideal of identities satisfied by the algebra of upper triangular $(n$´ n)-matrices.

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Last modified: March 24, 2011