dc.contributor Pascual Gainza, Pere dc.contributor.author Neras Lozano, Gerard dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I dc.date.accessioned 2015-02-13T09:48:39Z dc.date.available 2015-02-13T09:48:39Z dc.date.issued 2015-02 dc.identifier.uri http://hdl.handle.net/2099.1/25109 dc.description.abstract This thesis is an introduction to algebraic K-theory, focusing on the study of rings, although we will give some geometric interpretations and some relations to topological K-theory. We will study the K_0 group. The first two chapters of the thesis include some basic notions of rings and modules, and category theory, especially regarding abelian categories. Afterwards, we present projective modules and their properties, that will be used to define the K_0 group in Chapter 4. This chapter will include basic definitions and the main theorems of the Grothendieck group of a ring. We will also show some relations with vector bundles and topological K-theory. The last chapter introduces the K_0 group of a category with exact sequences and the G_0 group. It includes the proofs of three important abstract theorems about K_0 and the Fundamental Theorem of G_0. dc.language.iso eng dc.publisher Universitat Politècnica de Catalunya dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria K dc.subject.lcsh Grothendieck groups dc.subject.other Algebraic K-Theory dc.subject.other Grothendieck Groups dc.subject.other Projective Modules dc.subject.other Abelian Categories dc.title Introduction to Algebraic K - Theory dc.type Bachelor thesis dc.subject.lemac Grothendieck, Categories de dc.subject.ams Classificació AMS::19 K-theory::19A Grothendieck groups and $K_0$ dc.identifier.slug FME-1016 dc.rights.access Open Access dc.date.updated 2015-02-12T14:08:42Z dc.audience.educationlevel Grau dc.audience.mediator Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística dc.audience.degree GRAU EN MATEMÀTIQUES (Pla 2009)
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