# Hopfian and co-Hopfian objects.

Publicacions Matemàtiques (1992)

- Volume: 36, Issue: 1, page 293-317
- ISSN: 0214-1493

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topVaradarajan, Kalathoor. "Hopfian and co-Hopfian objects.." Publicacions Matemàtiques 36.1 (1992): 293-317. <http://eudml.org/doc/41149>.

@article{Varadarajan1992,

abstract = {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.},

author = {Varadarajan, Kalathoor},

journal = {Publicacions Matemàtiques},

keywords = {Anillos; Algebra de Hopf; Espacio de funciones continuas; Módulos; Hopficity; co-Hopficity; co-Hopfian as -module; Boolean ring; Boolean space; category Top; compact Hausdorff space; compact manifold},

language = {eng},

number = {1},

pages = {293-317},

title = {Hopfian and co-Hopfian objects.},

url = {http://eudml.org/doc/41149},

volume = {36},

year = {1992},

}

TY - JOUR

AU - Varadarajan, Kalathoor

TI - Hopfian and co-Hopfian objects.

JO - Publicacions Matemàtiques

PY - 1992

VL - 36

IS - 1

SP - 293

EP - 317

AB - 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.

LA - eng

KW - Anillos; Algebra de Hopf; Espacio de funciones continuas; Módulos; Hopficity; co-Hopficity; co-Hopfian as -module; Boolean ring; Boolean space; category Top; compact Hausdorff space; compact manifold

UR - http://eudml.org/doc/41149

ER -

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