FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 1, PAGES 257-266

On leading monomials of some T-ideals

V. V. Shchigolev

Abstract

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In this paper some analogs of the Gröbner base for T-ideals are considered. A sequence of normal monomials of the T-ideal $T$₂⁽³⁾ is built so that the monomials are independent w.r.t. the operation of monotonous substitution and the insertion operation. Also a theorem is proved stating that for algebras without $1$ a multilinear identity of the form $w$₁[x₁,x₂]w₂, where $x$₁, $x$₂ are variables and $w$₁, $w$₂ are monomials, belongs to every T-ideal that is finitely based w.r.t. the inclusion relation of the leading monomials.

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Last modified: May 10, 2001