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Valuations and Valuation Rings

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.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc663650
Date08 1900
CreatorsBadt, Sig H.
ContributorsVaughan, Nick H., Parrish, Herbert C.
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formativ, 42 leaves, Text
RightsPublic, Badt, Sig H., Copyright, Copyright is held by the author, unless otherwise noted. All rights

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