FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 2, PAGES 101-110

Combinatorial generators of the multilinear polynomial identities

V. N. Latyshev

Abstract

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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.

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Last modified: June 17, 2006