Hymo, John A.2014-03-142014-03-141990-05-14etd-09202005-090947http://hdl.handle.net/10919/39404In 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?v, 52 leavesBTDapplication/pdfenIn CopyrightLD5655.V856 1990.H966Number theory -- ResearchDissertationhttp://scholar.lib.vt.edu/theses/available/etd-09202005-090947/