Constructing universal Gröbner bases

  • Volker Weispfenning
Conference paper

DOI: 10.1007/3-540-51082-6_96

Part of the Lecture Notes in Computer Science book series (LNCS, volume 356)
Cite this paper as:
Weispfenning V. (1989) Constructing universal Gröbner bases. In: Huguet L., Poli A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1987. Lecture Notes in Computer Science, vol 356. Springer, Berlin, Heidelberg

Abstract

A universal Gröbner basis is a finite basis for a polynomial ideal that has the Gröbner property with respect to all admissible term-orders. Let R be a commutative polynomial ring over a field K, or more generally a non-commutative polynomial ring of solvable type over K (see [KRW]). We show, how to construct and characterize left, right, two-sided, and reduced universal Gröbner bases in R. Moreover, we extend the upper complexity bounds in [We4] to the construction of universal Gröbner bases. Finally, we prove the stability of universal Gröbner bases under specialization of coefficients. All these results have counterparts for polynomial rings over commutative regular rings (comp. [We3]).

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Volker Weispfenning
    • 1
  1. 1.Lehrstuhl für MathematikUniversität PassauPassauFRG

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