Geodesic
Finiteness of the standard basis of a~$T$-ideal containing Lie nilpotency of index~$4$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 75-85.

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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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V. N. Latyshev. Finiteness of the standard basis of a~$T$-ideal containing Lie nilpotency of index~$4$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 75-85. http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a4/

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