Miró-Roig, Rosa M. (Rosa Maria)Salat Moltó, Martí2017-07-042017-07-042017-01-16https://hdl.handle.net/2445/113296Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Rosa Maria Miró-RoigThe weak and strong Lefschetz properties on graded artinian algebras have been an object of study along the last few decades. Precisely, let be $A$ a graded artinian algebra. We say that $A$ has the Strong Lefschetz property (SLP) if the multiplication by a $d$th power of a general linear form have maximal rank (i.e. $\times L^{d} : A_{i} \rightarrow A_{i+d}$ is injective or surjective for every $i$). We say that $A$ has the Weak Lefschetz property (WLP) if occurs the same with $d = 1$. These properties have connections among different areas such as algebraic geometry, commutative algebra and combinatorics. Sometimes quite surprising, these connections give new approaches and relate problems, a priori, very distant.50 p.application/pdfengcc-by-nc-nd (c) Martí Salat Moltó, 2017http://creativecommons.org/licenses/by-nc-nd/3.0/esÀlgebra commutativaTreballs de fi de grauGeometria algebraicaSingularitats (Matemàtica)Anells artiniansCommutative algebraBachelor's thesesAlgebraic geometrySingularities (Mathematics)Artin ringsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess