Matroids algebraic over F(t) are algebraic over F (Q582298)

In his thesis [Oxford (1972)] \textit{M. J. Piff} conjectured that a matroid which is algebraic over a field F(t) with t transcendent over the field F must be algebraic over F. There are two unsatisfactory proofs of this conjecture given by the same author (1987) and by \textit{O. V. Shammeva} [Vestn. Mosk. Univ., Ser. I 1985, No.4, 29-32 (1985; Zbl 0579.05022)]. Now the author settled the conjecture by applying a theorem of Seidenberg about the number of algebraic systems with the coefficients in a ring \(I[a_ 1,...,a_ n]\) where \(I\in \{{\mathbb{Z}}\}\cup \{GF(p)/\) p a prime natural number\(\}\), having a solution in a field K containing I [see Zbl 0067.018].