We prove that certain class of Stanley–Reisner rings having sufficiently large multiplicities are Cohen–Macaulay using Alexander duality.

We give a purely combinatorial characterization of complete Stanley-Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.

Given an infinite field k and a simplicial complex Δ, common theme in studying the f- h-vectors of Δ has been consideration Hilbert series Stanley–Reisner ring k[Δ] modulo generic linear system parameters Θ. Historically, these computations have restricted to special classes complexes (most typically triangulations spheres or manifolds). We provide compact topological expression hd−1a(Δ), dimen...

For a graph G=(V,E) the edge ring k[G] is k[x1,…,xn]/I(G), where n=|V| and I(G) generated by {xixj;{i,j}∈E}. The conjecture we treat following.Conjecture 1. If has 2-linear resolution, then projective dimension of K[G], pd (k[G]), equals maximal degree vertex in G.As far as know, this first mentioned paper Gitler Valencia [7, Conjecture 4.13], there it called Eliahou-Villarreal conjecture. trea...

We survey the Stanley-Reisner correspondence in combinatorial commutative algebra, describing fundamental applications involving Alexander duality, associated primes, f and h-vectors, and Betti numbers of monomial ideals.