2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74811Let $K$ be an infinite field and $R=K[x_1,...,x_n]$ be the polynomial ring. Let $V=V_1, ..., V_m$ be a collection of vector spaces of linear forms. Denote by $A(V)$ the $K$-subalgebra of $R$ generated by the elements of the product $V_1... V_m$. Our goal is to investigate the properties of the algebra $A(V)$ and the relations with two problems in algebraic combinatorics White's and related conjectures on polymatroids and the study of integral posets.Commutative AlgebraCombinatorics13F50, 13P10, 5B35text