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Compactness in categories and its application in different categories

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dc.contributor.advisor Botha, S. G.
dc.contributor.advisor Alderton, Ian William, 1952- Thulapersad, Sarah 2015-01-23T04:24:21Z 2015-01-23T04:24:21Z 1994-12
dc.identifier.citation Thulapersad, Sarah (1994) Compactness in categories and its application in different categories, University of South Africa, Pretoria, <> en
dc.description.abstract In the paper [HSS] Herrlich, Salicrup and Strecker were able to show that Kuratowski / Mrowka's Theorem concerning compactness for topological spaces could be applied to a wider setting. In this dissertation, which is based on the paper [F subscript 1], we interpret Kuratowski / Mrowka's result in the category R-Mod. Chapter One deals mainly with the preliminary definitions and results and we also show that there is a 1-1 correspondence between torsion theories and standard factorisation systems. In Chapter Two we, obtain for every torsion theory T, a theory of T-compactness which is an extension of the definition of compactness found in [HSS]. We then obtain a characterisation of T-compactness under certain conditions on the ring R and torsion theory T. In Chapter Three we examine the class of T-compact R-modules more closely when the ring R is T-hereditary and T-noetherian. We also obtain further characterisation of T-compactness under these additional conditions. In Chapter Four we show that many topological results have analogues in R-Mod. en
dc.format.extent 1 online resource (111 leaves) en
dc.language.iso en
dc.subject Torsion theory en
dc.subject Radical en
dc.subject Factorisation structure en
dc.subject Hereditary en
dc.subject T-dense en
dc.subject T-closed en
dc.subject T-compact en
dc.subject T-hereditary en
dc.subject T-injective en
dc.subject T-noetherian en
dc.subject p-divisible en
dc.subject.ddc 512.55 THUL en
dc.subject.lcsh Categories (Mathematics) en
dc.title Compactness in categories and its application in different categories en
dc.type Dissertation
dc.description.department Mathematical Sciences M. Sc. (Mathematics)

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