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.

Location: http://mech.math.msu.su/~fpm/eng/k10/k103/k10310h.htm

Last modified: March 24, 2011