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 $4$.

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Last modified: October 18, 2012