Tournament of Books 2015
 
 

Special Offers see all

Enter to WIN a $100 Credit

Subscribe to PowellsBooks.news
for a chance to win.
Privacy Policy

Visit our stores


    Recently Viewed clear list


    Original Essays | January 6, 2015

    Matt Burgess: IMG 35 Seconds



    Late at night on September 22, 2014, at a housing project basketball court in Brooklyn, a white cop pushes a black man against a chain link fence.... Continue »

    spacer
Qualifying orders ship free.
$209.75
New Hardcover
Ships in 1 to 3 days
Add to Wishlist
available for shipping or prepaid pickup only
Available for In-store Pickup
in 7 to 12 days
Qty Store Section
25 Remote Warehouse Mathematics- Algebra

More copies of this ISBN

The Theory of Classical Valuations

by

The Theory of Classical Valuations Cover

 

Synopses & Reviews

Publisher Comments:

In his studies of cyclotomic fields, in view of establishing his monumental theorem about Fermat's last theorem, Kummer introduced "local" methods. They are concerned with divisibility of "ideal numbers" of cyclotomic fields by lambda = 1 - psi where psi is a primitive p-th root of 1 (p any odd prime). Henssel developed Kummer's ideas, constructed the field of p-adic numbers and proved the fundamental theorem known today. Kurschak formally introduced the concept of a valuation of a field, as being real valued functions on the set of non-zero elements of the field satisfying certain properties, like the p-adic valuations. Ostrowski, Hasse, Schmidt and others developed this theory and collectively, these topics form the primary focus of this book.

Synopsis:

Valuation theory is used constantly in algebraic number theory and field theory, and is currently gaining considerable research interest. Ribenboim fills a unique niche in the literature as he presents one of the first introductions to classical valuation theory in this up-to-date rendering of the authors long-standing experience with the applications of the theory. The presentation is fully up-to-date and will serve as a valuable resource for students and mathematicians.

Table of Contents

Absolute Values of Fields.- Valuations of a Field.- Polynomials and Henselian Valued Fields.- Extensions of Valuations.- Uniqueness of Extensions of Valuations and Poly-Complete Fields.- Extensions of Valuations: Numerical Relations.- Power Series and the Structure of Complete Valued Fields.- Decomposition and Inertia Theory.- Ramification Theory.- Valuation Characterization of Dedekind Domains.- Galois Groups of Algebraic Extensions of Infinite Degree.- Ideals, Valuations and Divisors in Algebraic Extensions of Infinite Degree of the Field of Rational Numbers.- A Glimpse on Krull Valuations.

Product Details

ISBN:
9780387985251
Author:
Ribenboim, Paulo
Author:
Ribenboim, P.
Author:
Ribenhoim, Paulo
Publisher:
Springer
Location:
New York :
Subject:
Algebra - General
Subject:
Fields, algebraic
Subject:
Algebraic fields
Subject:
Valuation theory
Subject:
K-theory
Subject:
Mathematics - Algebra
Subject:
Algebra - Abstract
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Undergraduate Texts in Mathematics
Publication Date:
May 1999
Binding:
HARDCOVER
Language:
English
Illustrations:
48
Pages:
414
Dimensions:
235 x 155 mm 1690 gr

Other books you might like

  1. Number Theory and Algebraic Geometry New Trade Paper $114.50
  2. Transcendental Number Theory New Trade Paper $67.25
  3. Applied Complex Variables... Used Trade Paper $10.00
  4. Prime Numbers: A Computational... New Hardcover $82.75

Related Subjects

Science and Mathematics » Electricity » General Electronics
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

The Theory of Classical Valuations New Hardcover
0 stars - 0 reviews
$209.75 In Stock
Product details 414 pages Springer-Verlag - English 9780387985251 Reviews:
"Synopsis" by , Valuation theory is used constantly in algebraic number theory and field theory, and is currently gaining considerable research interest. Ribenboim fills a unique niche in the literature as he presents one of the first introductions to classical valuation theory in this up-to-date rendering of the authors long-standing experience with the applications of the theory. The presentation is fully up-to-date and will serve as a valuable resource for students and mathematicians.
spacer
spacer
  • back to top

FOLLOW US ON...

     
Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.