A nonlinear algebraic matroid with infinite characteristic set (Q1080857)

If the characteristic set for vector representation of a matroid is infinite, it contains zero. The author shows that this need not be true for the algebraic characteristic set of a matroid, by proving that this set for Example 8 of \textit{A. W. Ingleton} [''Representations of matroids'', Combinat. Math. Appl. Proc. Conf. math. Inst., Oxford 1969, 149-167 (1971; Zbl 0222.05025)] is equal to the set of all prime numbers.