Science/Engineering Introduction to p-Adic Numbers and Valuation Theory (0120702681)

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George Bachman, "Introduction to p-Adic Numbers and Valuation Theory"

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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	Mathematics An Introduction to the Theory of Numbers This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary numbe ...
	Science/Engineering The Theory of Numbers: An Introduction Anthony A. Gioia, “The Theory of Numbers: An Introduction” Dover Publications \| 2001-03-28 \| ISBN: 0486414493 \| 226 pages \| DJVU \| 1,3 MB Support text for a first course in number theory features the use of algebraic methods for studyin ...
	Mathematics p-adic Numbers: An Introduction Author: Fernando Q. GouveaPublisher: SpringerPublish Date: 2003ISBN: 3540629114Pages: 302UniversitextThere are numbers of all kinds: rational, real, complex, p-adic... The p-adic numbers are less well known than the others, but they play a ...
	Technical P-adic Numbers, P-adic Analysis, and Zeta-functions Neal Koblitz, "P-adic Numbers, P-adic Analysis, and Zeta-functions" Springer-Verlag \| 1977 \| ISBN: 0387902740, 3540902740 \| 122 pages \| Djvu \| 1,4 MB These lecture notes are intended as an introduction to p -adic analysis on theelementa ...
	p-adic Numbers: An Introduction (Universitext) p-adic Numbers: An Introduction (Universitext)Springer \| 1997-07-04 \| ISBN: 3540629114 \| 306 pages \| PDF \| 4 MBFrom the reviews: "This is a well-written introduction to the world of p-adic numbers. The reader is led into the rich structure ...
	Technical An Introduction to the Theory of Numbers, 6 Ed G. H. Hardy, M. Wright, Andrew Wiles, "An Introduction to the Theory of Numbers, 6 Ed" Oxford University Press \| 2008 \| ISBN: 0199219869, 7115214271 \| 621 pages \| PDF \| 11,1 MB An Introduction to the Theory of Numbers by G. H. Hardy and ...

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	Mathematics An Introduction to the Theory of Numbers This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary numbe ...
	Science/Engineering The Theory of Numbers: An Introduction Anthony A. Gioia, “The Theory of Numbers: An Introduction” Dover Publications \| 2001-03-28 \| ISBN: 0486414493 \| 226 pages \| DJVU \| 1,3 MB Support text for a first course in number theory features the use of algebraic methods for studyin ...
	Mathematics p-adic Numbers: An Introduction Author: Fernando Q. GouveaPublisher: SpringerPublish Date: 2003ISBN: 3540629114Pages: 302UniversitextThere are numbers of all kinds: rational, real, complex, p-adic... The p-adic numbers are less well known than the others, but they play a ...
	Technical P-adic Numbers, P-adic Analysis, and Zeta-functions Neal Koblitz, "P-adic Numbers, P-adic Analysis, and Zeta-functions" Springer-Verlag \| 1977 \| ISBN: 0387902740, 3540902740 \| 122 pages \| Djvu \| 1,4 MB These lecture notes are intended as an introduction to p -adic analysis on theelementa ...
	p-adic Numbers: An Introduction (Universitext) p-adic Numbers: An Introduction (Universitext)Springer \| 1997-07-04 \| ISBN: 3540629114 \| 306 pages \| PDF \| 4 MBFrom the reviews: "This is a well-written introduction to the world of p-adic numbers. The reader is led into the rich structure ...
	Technical An Introduction to the Theory of Numbers, 6 Ed G. H. Hardy, M. Wright, Andrew Wiles, "An Introduction to the Theory of Numbers, 6 Ed" Oxford University Press \| 2008 \| ISBN: 0199219869, 7115214271 \| 621 pages \| PDF \| 11,1 MB An Introduction to the Theory of Numbers by G. H. Hardy and ...

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