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http://hdl.handle.net/11375/6203
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DC Field | Value | Language |
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dc.contributor.advisor | Banaschewski, Bernhard | en_US |
dc.contributor.author | Bhutani, Ravender Kiran | en_US |
dc.date.accessioned | 2014-06-18T16:34:27Z | - |
dc.date.available | 2014-06-18T16:34:27Z | - |
dc.date.created | 2010-04-05 | en_US |
dc.date.issued | 1983 | en_US |
dc.identifier.other | opendissertations/1531 | en_US |
dc.identifier.other | 2162 | en_US |
dc.identifier.other | 1262107 | en_US |
dc.identifier.uri | http://hdl.handle.net/11375/6203 | - |
dc.description.abstract | <p>This thesis is devoted to the study of Abelian Groups in the topos Shℒ of sheaves on a locale ℒ. The main topics considered are: injectivity, essential extensions of torsion groups, divisibility, purity, internal hom-functor, tensor product and flatness.</p> <p>We derive some general results about these notions. Also, we prove the Baer Criterion for injectivity in AbShℒ. For a well-ordered locale ℒ, we describe the injective hulls in AbShℒ and for some special locales we characterize the injectives in AbShℒ.</p> <p>We further discuss essential extensions of torsion groups and show amongst other things, that a first countable Hausdorff space X is discrete iff essential extensions in AbShX preserve torsion.</p> <p>Divisible groups are characterized here as absolutely pure groups. We discuss the internal adjointness between the tensor product and the internal hom-functor.</p> <p>Finally, we consider the notion of flatness, and show that the flat groups in AbShℒ are characterized the same way as in Ab, that is, flat = torsion free, and that A is flat in AbShℒ iff A* = [A,P] is an injective group, where P is an injective cogenerator.</p> | en_US |
dc.subject | Mathematics | en_US |
dc.subject | Mathematics | en_US |
dc.title | Abelian Groups in a Topos of Sheaves on a Locale | en_US |
dc.type | thesis | en_US |
dc.contributor.department | Mathematics | en_US |
dc.description.degree | Doctor of Philosophy (PhD) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
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File | Size | Format | |
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fulltext.pdf | 2.69 MB | Adobe PDF | View/Open |
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