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Combinatorica

, Volume 9, Issue 1, pp 107–109 | Cite as

Matroids algebraic overF(t) are algebraic overF

  • B. Lindström
Note

Abstract

In his thesis [3] M. J. Piff conjectured that a matroid, which is algebraic over a fieldFit) witht transcendent overF, must be algebraic overF. Two proofs have appeared, one by Shameeva [5] and another one by the author [2], but both are unsatisfactory. In this paper I will settle conjecture by applying a theorem of Seidenberg.

AMS subject classification (1980)

05 B 35 12 F 20 

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References

  1. [1]
    N. Jacobson,Basic Algebra I, Freeman & Co., New York, 1985.Google Scholar
  2. [2]
    B. Lindström, A reduction of algebraic representations of matroids,Proc. Amer. Math. Soc. 100 (1987), 388–389.Google Scholar
  3. [3]
    M. J.Piff, Some problems in combinatorial theory (thesis), Oxford, 1972.Google Scholar
  4. [4]
    A. Seidenberg, Some remarks on Hilbert's nullstellensatz,Archiv der Mathematik 7 (1956), 235–240.CrossRefGoogle Scholar
  5. [5]
    O. V. Shameeva, Algebraic representability. of matroids, Vestnik Moskovskogo Universiteta,Matematika 40 (1985), 29–32.Google Scholar

Copyright information

© Akadémiai Kiadó 1989

Authors and Affiliations

  • B. Lindström
    • 1
  1. 1.Department of MathematicsUniversity of StockholmStockholmSweden

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