Relatively Prime Gröbner Bases and Reducibility of S-Polynomials
Throughout, K shall denote a field. We show that a Gröbner basis G ⊆ K[X 1,..., X n ] has greatest common divisor 1 precisely if this holds for the set of leading power products of G. As a corollary a result of Buchberger concerning the reducibility of S-Polynomials to 0 can be refined to a necessary and sufficient criterion.
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