Construction of the Lindström valuation of an algebraic extension
Abstract Recently, Bollen, Draisma, and Pendavingh have introduced the Lindstrom valuation on the algebraic matroid of a field extension of characteristic p . Their construction passes through what they call a matroid flock and builds on some of the associated theory of matroid flocks which they develop. In this paper, we give a direct construction of the Lindstrom valuated matroid using the theory of inseparable field extensions. In particular, we give a description of the valuation, the valuated circuits, and the valuated cocircuits.