Propiedad Cohen-Macaulay en complejos simpliciales shellable

Abstract

[en] The main goal of this project is to prove the Stanley-Reisner ring of a shellable simplicial complex is Cohen-Macaulay over every field. To do so, we study the necessary theory from a non-homological standpoint in a selfcontained manner. In particular we study associated primes, dimension and grade of a module and how these pave the way for Cohen-Macaulay theory. We continue studying simplicial complexes and basic Stanley-Reisner theory, proving the needed results in order to prove our goal.