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}[x_{1},x_{2}]w_{2},
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