FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2004, VOLUME 10, NUMBER 4, PAGES 91-96

On noncommutative Gröbner bases over rings

E. S. Golod

Abstract

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Let $R$ be a commutative ring. It is proved that for verification whether a set of elements $\{f$_a} of the free associative algebra over $R$ is a Gröbner basis (with respect to some admissible monomial order) of the (bilateral) ideal that the elements $f$_a generate it is sufficient to check reducibility to zero of $S$-polynomials with respect to $\{f$_a} iff $R$ is an arithmetical ring. Some related open questions and examples are also discussed.

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Last modified: April 14, 2005