Irreducible elements in algebraic number fields

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dc.contributor.authorMcCoy, Daisy Coxen
dc.contributor.committeechairParry, Charles J.en
dc.contributor.committeememberBrown, E.en
dc.contributor.committeememberFarkas, Dianaen
dc.contributor.committeememberFletcher, P.en
dc.contributor.committeememberWheeler, Robert L.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:21:28Zen
dc.date.adate2005-10-19en
dc.date.available2014-03-14T21:21:28Zen
dc.date.issued1990en
dc.date.rdate2005-10-19en
dc.date.sdate2005-10-19en
dc.description.abstractThis dissertation is a study of two basic questions involving irreducible elements in algebraic number fields. The first question is: Given an algebraic integer β in a field with class number greater than two, how many different lengths of factorizations into irreducibles exist? The distribution into ideal classes of the prime ideals whose product is the principal ideal (β) determines the possible length of the factorizations into irreducibles. Chapter 2 gives precise answers when the field has class number 3 or 4, as well as when the class group is an elementary 2-group of order 8. The second question is: In a normal extension, when are there rational primes which split completely and remain irreducible? Chapter 3 focusses on the bicyclic bi-quadratic fields. The imaginary bicyclic biquadratic fields which contain such primes are completely determined.en
dc.description.degreePh. D.en
dc.format.extentiv, 76 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10192005-113254en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10192005-113254/en
dc.identifier.urihttp://hdl.handle.net/10919/39950en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1990.M4338.pdfen
dc.relation.isformatofOCLC# 23716384en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1990.M4338en
dc.subject.lcshAlgebraic number theoryen
dc.titleIrreducible elements in algebraic number fieldsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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