Matroids algebraic overF(t) are algebraic overF


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.

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    N. Jacobson,Basic Algebra I, Freeman & Co., New York, 1985.

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    B. Lindström, A reduction of algebraic representations of matroids,Proc. Amer. Math. Soc. 100 (1987), 388–389.

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    M. J.Piff, Some problems in combinatorial theory (thesis), Oxford, 1972.

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    A. Seidenberg, Some remarks on Hilbert's nullstellensatz,Archiv der Mathematik 7 (1956), 235–240.

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    O. V. Shameeva, Algebraic representability. of matroids, Vestnik Moskovskogo Universiteta,Matematika 40 (1985), 29–32.

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Lindström, B. Matroids algebraic overF(t) are algebraic overF . Combinatorica 9, 107–109 (1989).

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AMS subject classification (1980)

  • 05 B 35
  • 12 F 20