Type of Document Dissertation Author Hymo, John A. URN etd-09202005-090947 Title Problems involving relative integral bases for quartic number fields Degree PhD Department Mathematics Advisory Committee

Advisor Name Title Parry, Charles J. Committee Chair Brown, Ezra A. Committee Member McCoy, Robert A. Committee Member Rossi, John F. Committee Member Snider, Robert L. Committee Member Keywords

- Number theory research
Date of Defense 1990-05-14 Availability restricted AbstractIn 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?

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