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.

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