Thesis (M. Phil.)--University of Hong Kong, 1977.

published_or_final_version / Mathematics / Master / Master of Philosophy

This paper is an investigation of several basic properties of ordered Abelian groups, valuations, the relationship between valuation rings, valuations, and their value groups and valuation rings. The proofs to all theorems stated without proof can be found in Zariski and Samuel, Commutative Algebra, Vol. I, 1858. In Chapter I several basic theorems which are used in later proofs are stated without proof, and we prove several theorems on the structure of ordered Abelian groups, and the basic relationships between these groups, valuations, and their valuation rings in a field. In Chapter II we deal with valuation rings, and relate the structure of valuation rings to the structure of their value groups.

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 4, 2009) Vita. Includes bibliographical references.

No description available.

This thesis investigates some properties of valuations on fields. Basic definitions and theorems assumed are stated in Capter I. Chapter II introduces the concept of a valuation on a field. Real valuations and non-Archimedean valuations are presented. Chapter III generalizes non-Archimedean valuations. Examples are described in Chapters I and II. A result is the theorem stating that a real valuation of a field K is non-Archimedean if and only if $(a+b) < max4# (a), (b) for all a and b in K. Chapter III generally defines a non-Archimedean valuation as an ordered abelian group. Real non-Archimedean valuations are either discrete or nondiscrete. Chapter III shows that every valuation ring identifies a non-Archimedean valuation and every non-Archimedean valuation identifies a valuation ring.

The standard way of representing numbers on computers gives rise to errors which increase as computations progress. Using p-adic valuations can reduce error accumulation. Valuation theory tells us that p-adic and standard valuations cannot be directly compared. The p-adic valuation can, however, be used in an indirect way. This gives a method of doing arithmetic on a subset of the rational numbers without any error. This exactness is highly desirable, and can be used to solve certain kinds of problems which the standard valuation cannot conveniently handle. Programming a computer to use these p-adic numbers is not difficult, and in fact uses computer resources similar to the standard floating-point representation for real numbers. This thesis develops the theory of p-adic valuations, discusses their implementation, and gives some examples where p-adic numbers achieve better results than normal computer computation. / Graduation date: 1994

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 136-151).

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Orientador: Ricardo Luiz Coltro Antunes / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-08-06T14:05:14Z (GMT). No. of bitstreams: 1 Amorim_HenriqueJoseDomiciano_D.pdf: 817518 bytes, checksum: 6e551b7b266ab12c4b8220c127a09673 (MD5) Previous issue date: 2006 / Resumo: Esta tese de doutorado estuda as teorias do trabalho imaterial que o consagram hoje como força produtiva central. .As transformações nos processos de produção ativadas pela última reestruturação produtiva e o fim da bipolarização mundial abriram a possibilidade de reflexão em torno de atividades profissionais antes consideradas improdutivas. André Gorz e Antonio Negri, autores representativos hoje das teorias do trabalho imaterial, apreendem tais transformações a panir de uma problemática teórica comum: o desenvolvimento das forças produtivas e a qualificação profissional seriam os vetores centrais para a constituição de subjetividades político-revolucionárias ou anticapitalistas. Esta tese desenvolve a crítica de tais postulados / Abstract: This PhD Thesis studies the theories about immaterial work that put it as the main productive force. The transformations in the production processes activated bythe last productive restructuration and the end of the world bipolarization opened a possibility for reflection around ! professional activities previously considered unproductive. André Gorz and Antonio Negri, representative authors today of the theories of immaterial work, apprehend such transforrnations from a common theoretical problernatic: the development of the productive forces and the professional qualification are the central vectors to the constitution of political-revolutionary or anticapitalists subjectiveness. This thesis develops the criticism tO these postulates / Doutorado / Ciencias Sociais / Doutor em Ciências Sociais