On the Computation of Invariants in non-Normal, non-Pure Cubic Fields and in Their Normal Closures

dc.contributor.authorCline, Danny O.en
dc.contributor.committeechairParry, Charles J.en
dc.contributor.committeememberHaskell, Peter E.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberLinnell, Peter A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:18:51Zen
dc.date.adate2004-12-03en
dc.date.available2014-03-14T20:18:51Zen
dc.date.issued2004-11-17en
dc.date.rdate2007-12-03en
dc.date.sdate2004-11-21en
dc.description.abstractLet K=Q(theta) be the algebraic number field formed by adjoining theta to the rationals where theta is a real root of an irreducible monic cubic polynomial f(x) in Z[x]. If theta is not the cube root of a rational integer, we call the field K a non-pure cubic field, and if K doesn't contain the conjugates of theta, we call K a non-normal cubic field. A method described by Martinet and Payan allows us to construct such fields from elements of a quadratic field. In this work, we examine such non-normal, non-pure cubic fields and their normal closures, using algorithms in Mathematica to compute various invariants of these fields. In addition, we prove general results relating the ranks of the ideal class groups of the rings of integers of these cubic fields to those of their normal closures.en
dc.description.degreePh. D.en
dc.identifier.otheretd-11212004-230454en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-11212004-230454/en
dc.identifier.urihttp://hdl.handle.net/10919/29702en
dc.publisherVirginia Techen
dc.relation.haspartetd.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectCubic Fielden
dc.subjectIdeal Class Groupen
dc.subjectNormal Closureen
dc.titleOn the Computation of Invariants in non-Normal, non-Pure Cubic Fields and in Their Normal Closuresen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en
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