A reduction of algebraic representations of matroids
Abstract: We prove the following result conjectured by M. J. Piff in his thesis (1972).
Theorem. Let be a matroid with an algebraic representation over a field , where is transcendental over . Then has an algebraic representation over .
The proof depends on Noether's normalization theorem and the place extension theorem. We obtain the following corollary.
Corollary. If a matroid is algebraic over a field , then any minor of is algebraic over .
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