Guzmán Navarro, Ricardo MiguelArteaga Genes, Lina Paola2020-06-112020-06-112020-06-10https://repositorio.unicordoba.edu.co/handle/ucordoba/2891In this work an introductory study of module theory is made. A module is a structure defined analogously to a vectorial space but replacing the field by a ring. First, we provide some definitions, notations, and key necessary results which are going to help us with the understanding of the structure of finite generated modules (F.G.M) over a principal ideal domain (P.I.D). The focus of this project is the study of module theory, principally by using tools like ring theory and group theory. Finally, an application of the module decomposition theorem over P.I.D. to the Jordan and rational normal forms is presented, i.e. we are going to establish a connection between an important theorem of module theory and some linear algebra structures.Resumen ivAbstract vIntroducción 11. PRELIMINARES Y MÓDULOS 21.1. LEMA DE ZORN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2. ANILLOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3. MÓDULOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102. MÓDULOS SOBRE D.I.P 192.1. RESULTADOS PREVIOS . . . . . . . . . . . . . . . . . . . . . . . . 192.2. TEOREMA DE DESCOMPOSICIÓN DE MÓDULOS . . . . . . . . 463. FORMA CANÓNICA RACIONAL Y DE JORDAN 503.1. FORMA CANÓNICA RACIONAL Y FORMA CANÓNICA DE JORDAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2. FORMA CANÓNICA DE JORDAN . . . . . . . . . . . . . . . . . . 55Bibliografía 58application/pdfspaCopyright Universidad de Córdoba, 2020Trabajo de grado - Pregradoinfo:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 Internacional (CC BY-NC 4.0)MódulosDominio de ideales principalesForma canónica de JordanForma canónica racionalModulesMastery of major idealsRational canonical formJordan canonical form