Originally issued as the author's thesis, Dundee University. / Cover title. Bibliography: leaves [92-96].

The theory of function algebras has been an active field of research over the past two decades and its coming of age has been heralded by the appearance within the last twelve months of three textbooks devoted entirely to them, namely the books by Browder, Leibowitz and Gamelin. One of the attractive features of the theory of function algebras is that it draws on diverse specialities like the theory of Banach algebras, harmonic analysis and the theory of analytic functions of several complex variables. The last mentioned theory has led to some of the most powerful results in the theory of function algebras. Not surprisingly, many of these results, for example Rossi's local maximum modulus principle theorem 2.24, were first proved for finitely generated and then extended to arbitrary function algebras. This observation, together with the fact that there has been no systematic study of finitely generated function algebras, led to the writing of this thesis. We have made use of some of the results of the theory of analytic functions of several complex variables, though we have not specifically used the methods thereof. What we have looked for is ways in which the functions of finitely generated function algebras behave like analytic functions and then tried to see if arbitrarily generated function algebras behave in a similar way.

Thesis (Ph. D.)--University of Florida, 1993. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 150-168).

Dissertation (PhD)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

No description available.

Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2007. / 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 vertices. Algorithms are exhibited to construct these graphs in the case of n-step and -finite towers. These techniques are applied to find new tamely ramified n-step towers for 1 n 3. Various new tame towers are found, including a family of towers of cubic extensions for which numerical evidence suggests that it is asymptotically optimal over the finite field with p2 elements for each prime p 5. Families of wildly ramified Artin-Schreier towers over small finite fields which are candidates to be asymptotically good are also considered using our method.

Thesis (MSc)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

Orientador: Adriano Adrega de Moura / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-22T08:28:52Z (GMT). No. of bitstreams: 1 Calixto_LucasHenrique_M.pdf: 1707951 bytes, checksum: a7576ec9f19a4faf6e8bd959192baeb8 (MD5) Previous issue date: 2013 / Resumo: O principal objetivo dessa dissertação é explicar a classificação dos módulos irredutíveis de dimensão finita para qualquer super álgebra de funções sobre uma super álgebra de Lie básica. Os principais resultados dizem que um módulo irredutível de dimensão finita ou é uma representação de avaliação ou é um módulo de Kac para certo módulo de avaliação generalizado. Para chegar a tal objetivo, também fazemos uma revisão detalhada da classificação das super álgebras de Lie básicas / Abstract: The goal of this dissertation is to explain the classification of the irreducible finite-dimensional representations of a map superalgebra whose underlying simple Lie superalgebra is basic. The main result says that an irreducible finite-dimensional module is either an evaluation module or a Kac module associated to a certain generalized evaluation module. We also give a detailed review of the classification of the basic Lie superalgebras / Mestrado / Matematica / Mestre em Matemática

Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. / Class field theory describes the abelian extensions of a given field K in terms of various class groups of K, and can be viewed as one of the great successes of 20th century number theory. However, the main results in class field theory are pure existence results, and do not give explicit constructions of these abelian extensions. Such explicit constructions are possible for a variety of special cases, such as for the field Q of rational numbers, or for quadratic imaginary fields. When K is a global function field, however, there is a completely explicit description of the abelian extensions of K, utilising the theory of sign-normalised Drinfeld modules of rank one. In this thesis we give detailed survey of explicit class field theory for rational function fields over finite fields, and of the fundamental results needed to master this topic.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.