Valuations on Fields

PDF Version Also Available for Download.

Description

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 ... continued below

Physical Description

33 leaves

Creation Information

Walker, Catherine A. May 1977.

Context

This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. More information about this thesis can be viewed below.

Who

People and organizations associated with either the creation of this thesis or its content.

Chair

Committee Member

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Walker, Catherine A.

Provided By

UNT Libraries

The UNT Libraries serve the university and community by providing access to physical and online collections, fostering information literacy, supporting academic research, and much, much more.

Contact Us

What

Descriptive information to help identify this thesis. Follow the links below to find similar items on the Digital Library.

Degree Information

Description

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.

Physical Description

33 leaves

Subjects

Keywords

Library of Congress Subject Headings

Language

Identifier

Unique identifying numbers for this thesis in the Digital Library or other systems.

Collections

This thesis is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this thesis?

When

Dates and time periods associated with this thesis.

Creation Date

  • May 1977

Added to The UNT Digital Library

  • May 10, 2015, 6:16 a.m.

Description Last Updated

  • June 23, 2016, 3:54 p.m.

Usage Statistics

When was this thesis last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 8

Interact With This Thesis

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Walker, Catherine A. Valuations on Fields, thesis, May 1977; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc504040/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .