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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504040 |
| Date | 05 1900 |
| Creators | Walker, Catherine A. |
| Contributors | Vaughan, Nick H., Mohat, John T., 1924- |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | 33 leaves, Text |
| Rights | Public, Walker, Catherine A., Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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