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Dissertations / Theses on the topic 'Algebraic fields'

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Published: 4 June 2021

Last updated: 1 August 2024

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1

Hartsell, Melanie Lynne. "Algebraic Number Fields." Thesis, University of North Texas, 1991. https://digital.library.unt.edu/ark:/67531/metadc501201/.

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This thesis investigates various theorems on polynomials over the rationals, algebraic numbers, algebraic integers, and quadratic fields. The material selected in this study is more of a number theoretical aspect than that of an algebraic structural aspect. Therefore, the topics of divisibility, unique factorization, prime numbers, and the roots of certain polynomials have been chosen for primary consideration.

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2

Lötter, Ernest C. "On towers of function fields over finite fields /." Link to the online version, 2007. http://hdl.handle.net/10019.1/1283.

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3

Ganz, Jürg Werner. "Algebraic complexity in finite fields /." Zürich, 1994. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10867.

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4

Swanson, Colleen M. "Algebraic number fields and codes /." Connect to online version, 2006. http://ada.mtholyoke.edu/setr/websrc/pdfs/www/2006/172.pdf.

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5

Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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<p>This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions

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6

Rozario, Rebecca. "The Distribution of the Irreducibles in an Algebraic Number Field." Fogler Library, University of Maine, 2003. http://www.library.umaine.edu/theses/pdf/RozarioR2003.pdf.

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7

Alm, Johan. "Universal algebraic structures on polyvector fields." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-100775.

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The theory of operads is a conceptual framework that has become a kind of universal language, relating branches of topology and algebra. This thesis uses the operadic framework to study the derived algebraic properties of polyvector fields on manifolds.The thesis is divided into eight chapters. The first is an introduction to the thesis and the research field to which it belongs, while the second chapter surveys the basic mathematical results of the field.The third chapter is devoted to a novel construction of differential graded operads, generalizing an earlier construction due to Thomas Will

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8

Bode, Benjamin. "Knotted fields and real algebraic links." Thesis, University of Bristol, 2018. http://hdl.handle.net/1983/8527a201-2fba-4e7e-8481-3df228051413.

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This doctoral thesis offers a new approach to the construction of arbitrarily knotted configurations in physical systems. We describe an algorithm that given any link $L$ finds a function $f:mathbb{C}^2tomathbb{C}$, a polynomial in complex variables $u$, $v$ and the conjugate $overline{v}$, whose vanishing set $f^{-1}(0)$ intersects the unit three-sphere $S^3$ in $L$. These functions can often be manipulated to satisfy the physical constraints of the system in question. The explicit construction allows us to make precise statements about properties of these functions, such as the polynomial de

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9

McCoy, Daisy Cox. "Irreducible elements in algebraic number fields." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39950.

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10

Alnaser, Ala' Jamil. "Waring's problem in algebraic number fields." Diss., Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/2207.

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11

Lotter, Ernest Christiaan. "On towers of function fields over finite fields." Thesis, Stellenbosch : University of Stellenbosch, 2007. http://hdl.handle.net/10019.1/1283.

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Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2007.<br>Explicit towers of algebraic function fields over finite fields are studied by considering their ramification behaviour and complete splitting. While the majority of towers in the literature are recursively defined by a single defining equation in variable separated form at each step, we consider towers which may have different defining equations at each step and with arbitrary defining polynomials. The ramification and completely splitting loci are analysed by directed graphs with irreducible polynomials as vert

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12

Buyruk, Dilek. "On Algebraic Function Fields With Class Number Three." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613080/index.pdf.

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Let K/Fq be an algebraic function field with full constant field Fq and genus g. Then the divisor class number hK of K/Fq is the order of the quotient group, D0K /P(K), degree zero divisors of K over principal divisors of K. The classification of the function fields K with hK = 1 is done by MacRea, Leitzel, Madan and Queen and the classification of the extensions with class number two is done by Le Brigand. Determination of the necessary and the sufficient conditions for a function field to have class number three is done by H&uml<br>ulya T&uml<br>ore. Let k := Fq(T) be the rational function f

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13

RoÌˆer, Andrew. "On vector fields on singular algebraic surfaces." Thesis, University of Warwick, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415254.

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14

Alaca, Saban Carleton University Dissertation Mathematics and Statistics. "P-Integral bases of algebraic number fields." Ottawa, 1994.

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15

Han, Ilseop. "Tractibility of algebraic function fields in one variable over global fields /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9944223.

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16

Voloch, J. F. "Curves over finite fields." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355283.

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17

Hughes, Garry. "Distribution of additive functions in algebraic number fields." Title page, contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09SM/09smh893.pdf.

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18

Jogia, Danesh Michael Mathematics &amp Statistics Faculty of Science UNSW. "Algebraic aspects of integrability and reversibility in maps." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/40947.

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We study the cause of the signature over finite fields of integrability in two dimensional discrete dynamical systems by using theory from algebraic geometry. In particular the theory of elliptic curves is used to prove the major result of the thesis: that all birational maps that preserve an elliptic curve necessarily act on that elliptic curve as addition under the associated group law. Our result generalises special cases previously given in the literature. We apply this theorem to the specific cases when the ground fields are finite fields of prime order and the function field $mathbb{C}(t

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19

Kosick, Pamela. "Commutative semifields of odd order and planar Dembowski-Ostrom polynomials." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 104 p, 2010. http://proquest.umi.com/pqdweb?did=1992491941&sid=3&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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20

Riccomagno, Eva M. "Algebraic geometry in experimental design and related fields." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263314.

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21

Berardini, Elena. "Algebraic geometry codes from surfaces over finite fields." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0170.

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Nous proposons, dans cette thèse, une étude théorique des codes géométriques algébriques construits à partir de surfaces définies sur les corps finis. Nous prouvons des bornes inférieures pour la distance minimale des codes sur des surfaces dont le diviseur canonique est soit nef soit anti-strictement nef et sur des surfaces sans courbes irréductibles de petit genre. Nous améliorons ces bornes inférieures dans le cas des surfaces dont le nombre de Picard arithmétique est égal à un, des surfaces sans courbes de petite auto-intersection et des surfaces fibrées. Ensuite, nous appliquons ces borne

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22

Wuria, Muhammad Ameen Hussein. "Invariant algebraic surfaces in three dimensional vector fields." Thesis, University of Plymouth, 2016. http://hdl.handle.net/10026.1/4417.

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This work is devoted to investigating the behaviour of invariant algebraic curves for the two dimensional Lotka-Volterra systems and examining almost a geometrical approach for finding invariant algebraic surfaces in three dimensional Lotka-Volterra systems. We consider the twenty three cases of invariant algebraic curves found in Ollagnier (2001) of the two dimensional Lotka-Volterra system in the complex plane and then we explain the geometric nature of each curve, especially at the critical points of the mentioned system. We also investigate the local integrability of two dimensional Lotka-

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23

Abbott, John Anthony. "On the factorization of polynomials over algebraic fields." Thesis, University of Bath, 1988. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234672.

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24

Kribs, Richard A. "Fields with minimal discriminants : an empirical study." Virtual Press, 2005. http://liblink.bsu.edu/uhtbin/catkey/1314333.

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Modern algebra is a ubiquitous topic within mathematics and has many large and interconnected branches. Within algebra there is a branch known as field theory. Two measures of the complexity of a number field are its discriminant and signature. This paper correlates these two measures for fields of degree 4— 8 for which the discriminant is as small as possible. In studying the different ways minimal discriminants were located, an exponential relationship was noticed between the absolute value of the minimal discriminant and the signature. The actual absolute minimal discriminants and the expon

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25

曾紹祺 and Shiu-kei Tsang. "A survey on Golomb's Conjectures and Costas Arrays." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B42575345.

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26

Tsang, Shiu-kei. "A survey on Golomb's Conjectures and Costas Arrays." Click to view the E-thesis via HKUTO, 1999. http://sunzi.lib.hku.hk/hkuto/record/B42575345.

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27

Boulanger, Nicolas. "Algebraic aspects of gravity and higher spsin gauge fields." Doctoral thesis, Universite Libre de Bruxelles, 2003. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211290.

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28

Panario, Rodriguez Daniel Nelson. "Combinatorial and algebraic aspects of polynomials over finite fields." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0016/NQ28297.pdf.

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29

Grimm, David [Verfasser]. "Sums of Squares in Algebraic Function Fields / David Grimm." Konstanz : Bibliothek der Universität Konstanz, 2011. http://d-nb.info/1024034984/34.

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30

Cobbe, Alessandro. "Steinitz classes of tamely rami ed Galois extensions of algebraic number fields." Doctoral thesis, Scuola Normale Superiore, 2009. http://hdl.handle.net/11384/85661.

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31

Minardi, John. "Iwasawa modules for [p-adic]-extensions of algebraic number fields /." Thesis, Connect to this title online; UW restricted, 1986. http://hdl.handle.net/1773/5742.

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32

Pizzato, Marco. "Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements." Doctoral thesis, Università degli studi di Trento, 2013. https://hdl.handle.net/11572/367913.

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In this thesis we consider some problems concerning polynomials over finite fields. The first topic is the action of some groups on irreducible polynomials. We describe orbits and stabilizers. Next, we consider transformations of irreducible polynomials by quadratic and cubic maps and study the irreducibility of the polynomials obtained. Finally, starting from PN functions and monomials, we generalize this concept, introducing k-PN monomials and classifying them for small values of k and for fields of order p, p^2 and p^4.

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33

Pizzato, Marco. "Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements." Doctoral thesis, University of Trento, 2013. http://eprints-phd.biblio.unitn.it/1121/1/PizzatoPhDThesisbis.pdf.

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In this thesis we consider some problems concerning polynomials over finite fields. The first topic is the action of some groups on irreducible polynomials. We describe orbits and stabilizers. Next, we consider transformations of irreducible polynomials by quadratic and cubic maps and study the irreducibility of the polynomials obtained. Finally, starting from PN functions and monomials, we generalize this concept, introducing k-PN monomials and classifying them for small values of k and for fields of order p, p^2 and p^4.

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34

Beyronneau, Robert Lewis. "The solvability of polynomials by radicals: A search for unsolvable and solvable quintic examples." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2700.

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35

Ducet, Virgile. "Construction of algebraic curves with many rational points over finite fields." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4043/document.

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L'étude du nombre de points rationnels d'une courbe définie sur un corps fini se divise naturellement en deux cas : lorsque le genre est petit (typiquement g<=50), et lorsqu'il tend vers l'infini. Nous consacrons une partie de cette thèse à chacun de ces cas. Dans la première partie de notre étude nous expliquons comment calculer l'équation de n'importe quel revêtement abélien d'une courbe définie sur un corps fini. Nous utilisons pour cela la théorie explicite du corps de classe fournie par les extensions de Kummer et d'Artin-Schreier-Witt. Nous détaillons également un algorithme pour la r

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36

Aubertin, Bruce Lyndon. "Algebraic numbers and harmonic analysis in the p-series case." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/30282.

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For the case of compact groups G = Π∞ j=l Z(p)j which are direct products of countably many copies of a cyclic group of prime order p, links are established between the theories of uniqueness and spectral synthesis on the one hand, and the theory of algebraic numbers on the other, similar to the well-known results of Salem, Meyer et al on the circle. Let p ≥ 2 be a prime and let k{x⁻¹} denote the p-series field of formal Laurent series z = Σhj=₋∞ ajxj with coefficients in the field k = {0, 1,…, p-1} and the integer h arbitrary. Let L(z) = - ∞ if aj = 0 for all j; otherwise let L(z) be the

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37

Aleem, Hosam Abdel. "An algebraic approach to modelling the regulation of gene expression." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/an-algebraic-approach-to-modelling-the-regulation-of-gene-expression(d5d400b5-690e-4f32-9fd6-c80e4db455f3).html.

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Biotechnology is witnessing a remarkable growth evident both in the types of new products and in the innovative new processes developed. More efficient process design, optimisation and troubleshooting can be achieved through a better understanding of the underlying biological processes inside the cell; a key one of which is the regulation of gene expression. For engineers such understanding is attained through mathematical modelling, and the most commonly used models of gene expression regulation are those based on differential equations, as they give quantitative results. However, those resul

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38

Sorolla, Bardají Jordi. "On the algebraic limit cycles of quadratic systems." Doctoral thesis, Universitat Autònoma de Barcelona, 2005. http://hdl.handle.net/10803/3089.

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39

Lotter, Ernest Christiaan. "Explicit constructions of asymptotically good towers of function fields." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53417.

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Thesis (MSc)--Stellenbosch University, 2003<br>ENGLISH ABSTRACT: A tower of global function fields :F = (FI, F2' ... ) is an infinite tower of separable extensions of algebraic function fields of one variable such that the constituent function fields have the same (finite) field of constants and the genus of these tend to infinity. A study can be made of the asymptotic behaviour of the ratio of the number of places of degree one over the genus of FJWq as i tends to infinity. A tower is called asymptotically good if this limit is a positive number. The well-known Drinfeld- Vladut bound pr

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40

Gould, Miles. "Coherence for categorified operadic theories." Connect to e-thesis, 2008. http://theses.gla.ac.uk/689/.

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Thesis (Ph.D.) - University of Glasgow, 2008.<br>Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Mathematics, University of Glasgow, 2008. Includes bibliographical references. Print version also available.

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41

Hinkelmann, Franziska Babette. "Algebraic theory for discrete models in systems biology." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/28509.

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This dissertation develops algebraic theory for discrete models in systems biology. Many discrete model types can be translated into the framework of polynomial dynamical systems (PDS), that is, time- and state-discrete dynamical systems over a finite field where the transition function for each variable is given as a polynomial. This allows for using a range of theoretical and computational tools from computer algebra, which results in a powerful computational engine for model construction, parameter estimation, and analysis methods. Formal definitions and theorems for PDS and the concept of

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42

Hall-Seelig, Laura. "Asymptotically good towers of global function fields and bounds for the Ihara function." Amherst, Mass. : University of Massachusetts Amherst, 2009. http://scholarworks.umass.edu/dissertations/AAI3372263/.

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43

Lavallee, Melisa Jean. "Dihedral quintic fields with a power basis." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2788.

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Cryptography is defined to be the practice and studying of hiding information and is used in applications present today; examples include the security of ATM cards and computer passwords ([34]). In order to transform information to make it unreadable, one needs a series of algorithms. Many of these algorithms are based on elliptic curves because they require fewer bits. To use such algorithms, one must find the rational points on an elliptic curve. The study of Algebraic Number Theory, and in particular, rare objects known as power bases, help determine what these rational points are. With suc

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44

Krapp, Lothar Sebastian [Verfasser]. "Algebraic and Model Theoretic Properties of O-minimal Exponential Fields / Lothar Sebastian Krapp." Konstanz : KOPS Universität Konstanz, 2019. http://d-nb.info/1202012558/34.

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45

Mohamed, Mostafa Hosni [Verfasser]. "Algebraic decoding over finite and complex fields using reliability information / Mostafa Hosni Mohamed." Ulm : Universität Ulm, 2018. http://d-nb.info/1150781041/34.

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46

Kurtaran, Ozbudak Elif. "Results On Some Authentication Codes." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/2/12610350/index.pdf.

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In this thesis we study a class of authentication codes with secrecy. We obtain the maximum success probability of the impersonation attack and the maximum success probability of the substitution attack on these authentication codes with secrecy. Moreover we determine the level of secrecy provided by these authentication codes. Our methods are based on the theory of algebraic function fields over finite fields. We study a certain class of algebraic function fields over finite fields related to this class of authentication codes. We also determine the number of rational places of this class of

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47

Oi, Masao. "On ramifications of Artin-Schreier extensions of surfaces over algebraically closed fields of positive characteristic I." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/193564.

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JSIAM Letters Vol. 6 (2014) p.33-36<br>Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(理学)<br>甲第18639号<br>理博第4018号<br>新制||理||1579(附属図書館)<br>31553<br>京都大学大学院理学研究科数学・数理解析専攻<br>(主査)教授池田保, 教授雪江明彦, 教授上田哲生<br>学位規則第4条第1項該当

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48

Banaszak, Grzegorz. "Algebraic K-theory of number fields and rings of integers and the Stickelberger ideal /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487676261012829.

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49

Jacobs, G. Tony. "Reduced Ideals and Periodic Sequences in Pure Cubic Fields." Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc804842/.

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The “infrastructure” of quadratic fields is a body of theory developed by Dan Shanks, Richard Mollin and others, in which they relate “reduced ideals” in the rings and sub-rings of integers in quadratic fields with periodicity in continued fraction expansions of quadratic numbers. In this thesis, we develop cubic analogs for several infrastructure theorems. We work in the field K=Q(), where 3=m for some square-free integer m, not congruent to ±1, modulo 9. First, we generalize the definition of a reduced ideal so that it applies to K, or to any number field. Then we show that K has only finite

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50

Solanki, Nikesh. "Uniform companions for expansions of large differential fields." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/uniform-companions-for-expansions-of-large-differential-fields(a565a0d0-24b5-40a6-a414-5ead1631bc8d).html.

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