FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 1, PAGES 101-107

**Multiplicative orders on terms**

E. V. Gorbatov

Abstract

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Let $R$ be
a commutative ring with identity.
Any order on terms of the polynomial algebra $R[x$_{1},...,x_{k}]
induces in a natural way the notion of a leading term.
An order on terms is called multiplicative if and only if the leading
term of a product equals the product of leading terms.
In this paper, we present a procedure for the construction of
multiplicative orders.
We obtain some characterizations of rings for which such orders exist.
We give conditions sufficient for the existence of such orders.

Location: http://mech.math.msu.su/~fpm/eng/k07/k071/k07106h.htm

Last modified: December 21, 2006