Online Book on Valuation Theory (in progress)

On this website you will find preliminary versions of several chapters of my online book on Valuation Theory.

Warning: in some files, the first pages are (almost) blank. This is because chapters always start on a right hand page.

Please keep in mind that these versions are not final and subject to frequent change. In particular, the contents, references, page numbering, numbering of theorems and sections and even the numbering of the chapters is not at all final. Further, these versions still contain a number of mistakes and typos. Any suggestions for improvement and questions on the contents are highly welcome; please send them by email to: fvk [at] math.usask.ca.

Chapter 1: Ultrametric spaces (version of July 14, 2011)
(pdf file)

Chapter 2: Valued abelian groups (version of July 14, 2011)
(pdf file)

Chapter 3: Valued modules and vector spaces (version of July 14, 2011)
(pdf file)

Chapter 4: Valued fields (version of July 14, 2011)
(pdf file)

Chapter 5: Polynomials over valued fields (version of July 14, 2011)
(pdf file)

Chapter 6: Valued field extensions (version of July 14, 2011)
(pdf file)

Chapter 7: Ramification theory (version of July 14, 2011)
(pdf file)

Chapter 8: Immediate extensions (version of July 14, 2011)
(pdf file)

Chapter 9: Hensel's Lemma (version of July 14, 2011)
(pdf file)

Chapter 10: Orderings and valuations (version of July 14, 2011)
(pdf file)

Chapter 11: Defect (version of July 14, 2011)
(pdf file)

Chapter 12: Additive polynomials (version of July 14, 2011)
(pdf file)

Chapter 13: The tame and the wild valuation theory (version of July 14, 2011)
(pdf file)

Chapter 14: Extremality, maximality, and defectless fields (version of July 14, 2011)
(pdf file)

Chapter 24: Preliminaries from algebra (version of July 14, 2011)
(pdf file)

Last update: March 28, 2023