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/

[1] Volichenko I. B., $T$-ideal, porozhdënnyi elementom $[x_1,x_2,x_3,x_4]$, Preprint, In-t mat. AN BSSR, Minsk, 1978

[2] Kemer A. R., “Konechnye bazisy tozhdestv assotsiativnykh algebr”, Algebra i logika, 26 (1987), 597–641 | MR | Zbl

[3] Latyshev V. N., “O konechnoi porozhdënnosti $T$-ideala s elementom $[x_1,x_2,x_3,x_4]$”, Sib. mat. zhurn., 6:6 (1965), 1432–1434 | Zbl

[4] Latyshev V. N., “Kombinatornye porozhdayuschie polilineinykh polinomialnykh tozhdestv”, Fundament. i prikl. mat., 12:2 (2006), 101–110 | MR | Zbl

[5] Higman G., “Ordering by divisibility in abstract algebras”, Proc. Lond. Math. Soc., 2 (1952), 326–336 | DOI | MR | Zbl

[6] Specht W., “Gesetze in Ringen”, Math. Z., 52 (1950), 557–589 | DOI | MR | Zbl