Matroids algebraic overF(t) are algebraic overF
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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.
[1] N. Jacobson,et al. Basic Algebra I , 1976 .
[2] A reduction of algebraic representations of matroids , 1987 .
[3] N. Jacobson,et al. Basic Algebra II , 1989 .
[4] A. Seidenberg. Some remarks on Hilbert's Nullstellensatz , 1956 .