Introduction to p-Adic Numbers and Valuation Theory

George Bachman, "Introduction to p-Adic Numbers and Valuation Theory"
Academic Press | 1964 | ISBN: 0120702681 | 173 pages | Djvu | 3 MB

The field of p-zdic numbers, which can be obtained from the
field of rational numbers by a completion process with respect
to a special kind of mapping, or valuation, similar in many respects
to the ordinary absolute value mapping has a great number of
interesting properties. However, beyond this, it turns out that
such fields are of particular interest and importance in algebraic
number theory and in algebraic geometry. This is equally true
of the general notion of a valuation together with some of its
related concepts.
The book is meant to serve as an introduction to valuation
theory. The first two chapters have been written mainly for
advanced undergraduate students and first year graduate students.
The amount of algebra required is quite small, and the algebraic
results needed for these two chapters are included in the first
four sections of the appendix. It is hoped that in this fashion
these two chapters will be reasonably self-contained and available
to as wide an audience as possible. In addition, exercises have
been added to these chapters most of which are intended to give
the reader some manipulative facility with the concepts intro-
introduced.
The remaining three chapters definitely demand more mathe-
mathematical maturity on the part of the reader. At least a first course
in modern algebra would be required to read parts of them.
Although most of the material needed for these chapters has been
stated in the appendix, this is meant just to serve as a handy
glossary for the reader. References have been supplied for this
material

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