  Using linear algebra methods we study certain algebraic properties of
monomial rings and matroids. Let I be a monomial ideal in a polynomial ring
over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the
normalization of the Rees algebra of I in terms of an Ehrhart ring. We
introduce the basis Rees cone of a matroid (or a polymatroid) and study their
facets. Some applications to Rees algebras are presented. It is shown that the
basis monomial ideal of a matroid (or a polymatroid) is normal.
