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
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