GRASSMANN-PLUCKER RELATIONS AND MATROIDS WITH COEFFICIENTS

Matroids with coefficients in a fuzzy ring have been introduced in [A. W. M. Dress, Adv. in Math. 59 (1986), 97-123]. Based on this paper and [A. W. M. Dress and W. Wenzel, Adv. in Math. 77 (1989), 1-36] we will show here that a matroid with coefficients of finite rank can also be defined in terms of its associated Grassmann-Plücker map, which-in a way-generalizes classical determinants. More precisely, we will show that such matroids correspond naturally and in a one-to-one fashion to equivalence classes of appropriately defined Grassmann-Plücker maps. © 1991.