Un ejemplo de teoría de homotopia en los grupos abelianos
For a commutative unitary ring R, we have developed a new homotopy theory in the category of abelian groups. The homotopy category of this theory has the following property: if an abelian group A admits the structrure of an R-module, then A has the homotopy type of the zero abelian group. As a co...
Guardado en:
| Autor principal: | |
|---|---|
| Otros Autores: | |
| Formato: | text (thesis) |
| Lenguaje: | spa |
| Publicado: |
Universidad de Zaragoza (España)
1980
|
| Materias: | |
| Acceso en línea: | https://dialnet.unirioja.es/servlet/oaites?codigo=1499 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | For a commutative unitary ring R, we have developed a new homotopy theory in the category of abelian groups. The homotopy category of this theory has the following property: if an abelian group A admits the structrure of an R-module, then A has the homotopy type of the zero abelian group. As a consequence of this fact, this theory is a useful tool to analyze the obstruction of an abelian group to be an R-module.
This work contains a detailed study of the analogues of homotopy groups and the construction of homotopy sequences associated to a homomorphism of abelian groups. We have also analyzed the theories associated to
some particular rings, for example, for the ring of rational numbers, Q, we have the following version of the Whitehead theorem: An abelian group A has the structure of a Q-module ( A is contractible) if and only if A has trivial homotopy groups. |
|---|