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 $4$. 
@article{FPM_2012_17_5_a4,
     author = {V. N. Latyshev},
     title = {Finiteness of the standard basis of a~$T$-ideal containing {Lie} nilpotency of index~$4$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {75--85},
     publisher = {mathdoc},
     volume = {17},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a4/}
}
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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/