Finite dimensional division algebras over a field

dc.contributor.advisorByrd, Richard D.
dc.contributor.committeeMemberFitzgibbon, William E., III
dc.contributor.committeeMemberLloyd, Justin T.
dc.contributor.committeeMemberYoes, M. G., Jr.
dc.creatorNakamura-Sundnas, Mitsue
dc.date.accessioned2024-01-05T20:33:05Z
dc.date.available2024-01-05T20:33:05Z
dc.date.copyright1990-09-13
dc.date.issued1987
dc.description.abstractThe problem of characterizing all division algebras over the field of real numbers has occupied algebraists since the discovery of the quaternions by Hamilton in 1843, and the discovery of the Caley numbers by Caley in 1845. In 1878, Frobenius proved that the only associative division algebras over the field of real numbers were the field of real numbers, the field of complex numbers, or the division algebra of real quaternions. Next, in 1940, Heinz Hopf showed that the dimension of any division algebra over the field of real numbers had to be a power of 2. Finally, Raul Bott and John Milnor, and independently M. Kervaire, showed that the only possible dimensions of any division algebra over the field of real numbers were 1, 2, 4, and 8. In this text, we will show that we can always find an associative division algebra of any dimension n e IN over a finite field. We will also discuss the finite dimensional associative division algebras over the field of real numbers by presenting the result of Frobenius.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other18434086
dc.identifier.urihttps://hdl.handle.net/10657/15799
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.subjectFinite fields (Algebra)
dc.titleFinite dimensional division algebras over a field
dc.type.dcmiText
dc.type.genreThesis
dcterms.accessRightsThe full text of this item is not available at this time because it contains documents that are presumed to be under copyright and are accessible only to users who have an active CougarNet ID. This item will continue to be made available through interlibrary loan.
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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