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. © 2008 Elsevier Inc. All rights reserved.
Villarreal, R. H. (2008). Rees cones and monomial rings of matroids. Linear Algebra and Its Applications, 428(11–12), 2933–2940. https://doi.org/10.1016/j.laa.2008.01.035