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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k062/k06206h.htm

Last modified: June 17, 2006