Teorema de descomposición de módulos sobre dominios de ideales principales
In 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...
- Autores:
-
Arteaga Genes, Lina Paola
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2020
- Institución:
- Universidad de Córdoba
- Repositorio:
- Repositorio Institucional Unicórdoba
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unicordoba.edu.co:ucordoba/2891
- Acceso en línea:
- https://repositorio.unicordoba.edu.co/handle/ucordoba/2891
- Palabra clave:
- Módulos
Dominio de ideales principales
Forma canónica de Jordan
Forma canónica racional
Modules
Mastery of major ideals
Rational canonical form
Jordan canonical form
- Rights
- restrictedAccess
- License
- Copyright Universidad de Córdoba, 2020
| Summary: | In 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. |
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