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- W2406600618 abstract "The aim ofthe presentpaper isto study Hopfian and Co-Hopfian objects incategorieslikethe category of rings,the module categoriesA-mod and mod-A forany ring A . Using Stone'srepresentationtheorem any Boolean ringcan be regarded as the ringA of clopen subsetsof a compact Hausdorff totallydisconnected space X . Itturns out that the Boolean ring A willbe Hopfian (resp. co-Hopfian) ifand only ifthe space X isco-Hopfian (resp. Hopfian)in the category Top.For any compact Hausdorff space X let C7,(X)(resp .Cc(X)) denote the R(resp .C)-algebraof real(resp. complex) valued continuous functionson X . Using Celfand'srepresentationtheorem we willprove that C7?(X)(Ce(X)) isHopfian (respectivelyco-Hopfian) as an R(C)- algebra ifand only ifX is co-Hopfian (respectivelyHopfian) as an object of Top. We also study Hopfian and co-Hopfian compact topologicalmanifolds." @default.
- W2406600618 created "2016-06-24" @default.
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- W2406600618 date "1992-01-01" @default.
- W2406600618 modified "2023-09-27" @default.
- W2406600618 title "A bstract HOPFIAN AND CO-HOPFIAN OBJECTS" @default.
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