Relatively Prime Gröbner Bases and Reducibility of S-Polynomials

Alexander Kovačec
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Alexander Kovačec: Johanes Kepler Universität Linz, Research Institute for Symbolic Computation (RISC)

A chapter in Lattices, Semigroups, and Universal Algebra, 1990, pp 143-146 from Springer

Abstract: Abstract 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.

Date: 1990
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DOI: 10.1007/978-1-4899-2608-1_16

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