FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 5, PAGES 75-85

**Finiteness of the standard basis of
a $T$-ideal containing Lie nilpotency of
index $4$**

V. N. Latyshev

Abstract

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Recently the author presented a notion of standard basis for
a $T$-ideal
of the free associative algebra over a field of zero
characteristic.
It was proved that it is finite if the $T$-ideal contains either Lie
nilpotency of index $3$ or a multilinear
product of commutators of degree $2$.
Here we prove the finiteness of the reduced standard basis of any
$T$-ideal
containing Lie nilpotency of index $4$.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k115/k11505h.htm

Last modified: October 18, 2012