Title page for ETD etd-09202005-090947


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
Abstract

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?

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