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Closure relations, Buchberger's algorithm, and polynomials in infinitely many variables

  • Daniel E. Cohen
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 270)

Keywords

Partial Order Power Product Polynomial Ring Total Order Finite Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Buchberger B (1965) Ein Algorithmus zum Auffinden der Basiselemente des Restkiassenringes nach einem null-dimensionalen Polynomideal. Ph. D. thesis, University of Innsbruck, Austria.Google Scholar
  2. Buchberger B (1970) Ein algorithmisches Kriterium für die Lösbarkeit eines algebraisches Gleichunssystems. Aequationes Mathematicae 4: 374–383.Google Scholar
  3. Buchberger B (1976) A theoretical basis for the reduction of polynomials to canonical form. ACM SIGSAM Bull. 10/3: 19–29.Google Scholar
  4. Buchberger B (1983) A critical-pair completion algorithm in reduction rings. Technical report CAMP 83-21.O. Math. Institute, University of Linz, AustriaGoogle Scholar
  5. Buchberger B (1984) A critical-pair completion algorithm for finitely generated ideals in rings. In: Börger E et al. (eds) Logic and machines: decison problems and complexity. Lecture Notes in Computer Science 171. Springer, Berlin Heidelberg New YorkGoogle Scholar
  6. Cohen DE (1967) On the laws of a metabelian variety. Journal of Algebra 5: 267–273.Google Scholar
  7. Dickson L. (1913) Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. American J. Math. 35: 413–422.Google Scholar
  8. Emmott P (1987) Ph. D. thesis, Queen Mary College, London University.Google Scholar
  9. Higman G (1952) Ordering by divisibility in abstract algebras. Proc London Math. Soc. (3) 2: 326–336.Google Scholar
  10. Kruskal JB (1972) The theory of well-quasi-ordering: a frequently discovered concept. J. Combinatorial Theory A 13: 297–305.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Daniel E. Cohen
    • 1
  1. 1.Mathematics DepartmentQueen Mary CollegeLondon

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