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dc.contributor.authorNafari, Manizhehen_US
dc.date.accessioned2011-10-11T20:49:03Z
dc.date.available2011-10-11T20:49:03Z
dc.date.issued2011-10-11
dc.date.submittedJanuary 2011en_US
dc.identifier.otherDISS-11335en_US
dc.identifier.urihttp://hdl.handle.net/10106/6190
dc.description.abstractM. Artin, W. Schelter, J. Tate, and M. Van den Bergh introduced the notion of non-commutative regular algebras, and classified regular algebras of global dimension 3 on degree-one generators by using geometry (i.e., point schemes) in the late 1980s. Recently, T. Cassidy and M. Vancliff generalized the notion of a graded Clifford algebra and called it a graded skew Clifford algebra.In this thesis, we prove that all classes of quadratic regular algebras of global dimension 3 contain graded skew Clifford algebras or Ore extensions of graded skew Clifford algebras of global dimension 2. We also prove that some regular algebras of global dimension 4 can be obtained from Ore extensions of regular graded skew Clifford algebras of global dimension 3. We also show that a certain subalgebra R of a regular graded skew Clifford algebra A is a twist of the polynomial ring if A is a twist of a regular graded Clifford algebra B. We have an example that demonstrates that this can fail when A is not a twist of B.en_US
dc.description.sponsorshipVancliff, Michaelaen_US
dc.language.isoenen_US
dc.publisherMathematicsen_US
dc.titleRegular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimensionen_US
dc.typePh.D.en_US
dc.contributor.committeeChairVancliff, Michaelaen_US
dc.degree.departmentMathematicsen_US
dc.degree.disciplineMathematicsen_US
dc.degree.grantorUniversity of Texas at Arlingtonen_US
dc.degree.leveldoctoralen_US
dc.degree.namePh.D.en_US


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