Zarzuela, SantiagoÚbeda Ripoll, Pol2023-06-132023-06-132023-01-24https://hdl.handle.net/2445/199123Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Santiago Zarzuela[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.49 p.application/pdfspacc-by-nc-nd (c) Pol Úbeda Ripoll, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Combinatòria (Matemàtica)Treballs de fi de grauAnells commutatiusAnells localsCombinationsBachelor's thesesCommutative ringsLocal ringsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess