Geodesic
Combinatorial generators of the multilinear polynomial identities
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 101-110 
V. N. Latyshev. Combinatorial generators of the multilinear polynomial identities. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 101-110. http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a6/
@article{FPM_2006_12_2_a6,
     author = {V. N. Latyshev},
     title = {Combinatorial generators of the multilinear polynomial identities},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {101--110},
     year = {2006},
     volume = {12},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a6/}
}
TY  - JOUR
AU  - V. N. Latyshev
TI  - Combinatorial generators of the multilinear polynomial identities
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2006
SP  - 101
EP  - 110
VL  - 12
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a6/
LA  - ru
ID  - FPM_2006_12_2_a6
ER  - 
%0 Journal Article
%A V. N. Latyshev
%T Combinatorial generators of the multilinear polynomial identities
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2006
%P 101-110
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a6/
%G ru
%F FPM_2006_12_2_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

A Gröbner–Shirshov basis (a combinatorial system of generators) is defined in the set of multilinear elements of a T-ideal of the free associative algebra with a countable set of indeterminates. A combinatorial version of the well-known Specht problem about the finite basedness of polynomial identities of an arbitrary associative algebra is formulated. A “combinatorial Spechtness” property of the multilinear product of commutators of degree 2 and the same property for the three-linear commutator are established.

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

[2] Kemer A. R., Idealy tozhdestv assotsiativnykh algebr, Nauka, Barnaul, 1988 | Zbl

[3] Latyshev V. N., “O shpekhtovosti nekotorykh mnogoobrazii assotsiativnykh algebr”, Algebra i logika, 8:6 (1969), 660–673 | Zbl

[4] Latyshev V. N., “Chastichno uporyadochennye mnozhestva i nematrichnye tozhdestva assotsiativnykh algebr”, Algebra i logika, 15:1 (1976), 53–70 | Zbl

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

[6] Kanel-Belov A., Rowen L. H., “Computational Aspects of Polynomial Identities Wellesleg”, Research Notes in Math., 9, 2004 | MR

[7] Latyshev V. N., “A general version of standard basis and its application to T-ideals”, Acta Appl. Math., 85 (2005), 219–221 | DOI | MR | Zbl

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