A constructive nullstellensatz for univariate polynomials
dc.contributor | Wang, James L. | |
dc.contributor | Moore, Robert L. | |
dc.contributor | Kwon, Hyun-Kyoung | |
dc.contributor | Roskos-Ewoldsen, Beverly | |
dc.contributor.advisor | Trent, Tavan T. | |
dc.contributor.author | Netyanun, Anupan | |
dc.contributor.other | University of Alabama Tuscaloosa | |
dc.date.accessioned | 2017-03-01T17:00:32Z | |
dc.date.available | 2017-03-01T17:00:32Z | |
dc.date.issued | 2014 | |
dc.description | Electronic Thesis or Dissertation | en_US |
dc.description.abstract | In 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.extent | 43 p. | |
dc.format.medium | electronic | |
dc.format.mimetype | application/pdf | |
dc.identifier.other | u0015_0000001_0001537 | |
dc.identifier.other | Netyanun_alatus_0004D_11842 | |
dc.identifier.uri | https://ir.ua.edu/handle/123456789/1994 | |
dc.language | English | |
dc.language.iso | en_US | |
dc.publisher | University of Alabama Libraries | |
dc.relation.hasversion | born digital | |
dc.relation.ispartof | The University of Alabama Electronic Theses and Dissertations | |
dc.relation.ispartof | The University of Alabama Libraries Digital Collections | |
dc.rights | All rights reserved by the author unless otherwise indicated. | en_US |
dc.subject | Mathematics | |
dc.title | A constructive nullstellensatz for univariate polynomials | en_US |
dc.type | thesis | |
dc.type | text | |
etdms.degree.department | University of Alabama. Department of Mathematics | |
etdms.degree.discipline | Mathematics | |
etdms.degree.grantor | The University of Alabama | |
etdms.degree.level | doctoral | |
etdms.degree.name | Ph.D. |
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