Valuations on Fields

• Main Author: Walker, Catherine A.
• Other Authors: Vaughan, Nick H.
• Format: Others
• Language: English
• Published: North Texas State University 1977
• Subjects: real valuations; Algebraic fields.; Valuation theory.; non-Archimedean valuations
• Online Access: https://digital.library.unt.edu/ark:/67531/metadc504040/

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.