A constructive nullstellensatz for univariate polynomials

dc.contributorWang, James L.
dc.contributorMoore, Robert L.
dc.contributorKwon, Hyun-Kyoung
dc.contributorRoskos-Ewoldsen, Beverly
dc.contributor.advisorTrent, Tavan T.
dc.contributor.authorNetyanun, Anupan
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-03-01T17:00:32Z
dc.date.available2017-03-01T17:00:32Z
dc.date.issued2014
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractIn this dissertation, we will take an effective approach to prove the Hilbert's Nullstellensatz in a special case where we have univariate polynomials $f_{i}(z)'s$ for $i\in\{1,2,...,m\}$. This approach will explicitly construct polynomials $p_{i}(z)'s$ for $i\in\{1,2,...,m\}.$ Moreover, we will get the best result on the bounds for the degrees of polynomials $p_{i}(z)'s.$ We then use a similar technique to solve the problems in a matrix case. Previous work motivated by algebraic techniques are from {[}2{]} W.D.Brownawell, {[}5{]} J.Kollar. They made a big improvement on the bounded degree of $p_{i}(z)'s$ in solutions. We are also motivated by works done in analysis from L. Carleson (1962), T. Wolff (1979). These are used to get the best result on the bounds on the degrees of $p_{i}'s$ in the solutions obtained in this dissertation. For the matrix case, we are motivated by {[}11{]} T.T. Trent, X. Zhang. This will enable us to derive the results in the matrix case.en_US
dc.format.extent43 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0001537
dc.identifier.otherNetyanun_alatus_0004D_11842
dc.identifier.urihttps://ir.ua.edu/handle/123456789/1994
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleA constructive nullstellensatz for univariate polynomialsen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.
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