FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 3, PAGES 127-134

Distributivity, binary relations, and standard bases

E. S. Golod

Abstract

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In the author's previous papers, the connection between generating syzygy modules by binary relations, the property of a commutative ring to be arithmetical (that is to have a distributive ideal lattice), and the use of the so-called S-polynomials in the standard basis theory were discussed. In this note, these connections are considered in a more general context. As an illustration of the usefulness of these considerations, a simple proof of some well-known fact from commutative algebra is given.

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