Problems involving relative integral bases for quartic number fields
In this dissertation the question of whether or not a relative extension of number fields has a relative integral basis is considered. In Chapters 2 and 3 we use a criteria of Mann to determine when a cyclic quartic field or a pure quartic field has an integral basis over its quadratic subfield. In...
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| Format: | Others |
| Language: | en |
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Virginia Tech
2014
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| Online Access: | http://hdl.handle.net/10919/39404 http://scholar.lib.vt.edu/theses/available/etd-09202005-090947/ |
| Summary: | In this dissertation the question of whether or not a relative extension of number fields has a relative integral basis is considered. In Chapters 2 and 3 we use a criteria of Mann to determine when a cyclic quartic field or a pure quartic field has an integral basis over its quadratic subfield. In the final chapter we study the question: if the relative discriminant of an extension K / k is principal, where [K : k] = l such that l is an odd prime and k is either a quadratic or a normal quartic number field, does K / k have an integral basis? === Ph. D. |
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