Relatively Prime Gröbner Bases and Reducibility of S-Polynomials

  • Alexander Kovačec


Throughout, K shall denote a field. We show that a Gröbner basis GK[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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  1. B Buchberger B. “Gröbner Bases: An Algorithm Approach to Polynomial Ideal Theory”, p. 184-232 in N. K. Bose (ed.): Multidimensional System Theory, Reidel (1985).Google Scholar
  2. H Hungerford T. Algebra, Graduate Texts in Mathematics 73, Springer (1974).Google Scholar
  3. K Kovačec A. “ Buchberger’s Theory of Gröbner bases”, unpublished LATEX notes written at occasion of the Algebra-conference at Lisbon/Portugal, June 1988.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Alexander Kovačec
    • 1
    • 2
  1. 1.Research Institute for Symbolic Computation (RISC)Johanes Kepler Universität LinzLinz AuhofAustria
  2. 2.Travessa Ladeira do SeminárioCoimbraPortugal

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