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INICIO |
27 de julio de 2024
Hopfian and co-Hopfian objects.
| Título inglés | Hopfian and co-Hopfian objects. |
|---|---|
| Título español | Objetos hopfianos y co-hopfianos. |
| Autor/es | Varadarajan, Kalathoor |
| Organización | Univ. Calgary, Calgary (Alberta), Canadá |
| Revista | 0214-1493 |
| Publicación | 1992, 36 (1): 293-317, 25 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | The aim of the present paper is to study Hopfian and Co-Hopfian objects in categories like the category of rings, the module categories A-mod and mod-A for any ring A. Using Stone's representation theorem any Boolean ring can be regarded as the ring A of clopen subsets of compact Hausdorff totally disconnected space X. It turns out that the Boolean ring A will be Hopfian (resp. co-Hopfian) if and only if the space X is co-Hopfian (resp. Hopfian) in the category Top. For any compact Hausdorff space X let CR(X) (resp. CC(X)) denote the R (resp. C)-algebra of real (resp. complex) valued continuous functions on X. Using Gelfand's representation theorem we will prove that CR(X) (CC(X)) is Hopfian (respectively co-Hopfian) as an R(C) algebra if and only if X is co-Hopfian (respectively Hopfian) as an object of Top. We also study Hopfian and co-Hopfian compact topological manifolds. |
| Clasificación UNESCO | 120105 |
| Palabras clave español | Anillos ; Algebra de Hopf ; Espacio de funciones continuas ; Módulos |
 Acceso al artículo completo |
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