BN.com Gift Guide

The Theory of Classical Valuations / Edition 1

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $29.69
Usually ships in 1-2 business days
(Save 85%)
Other sellers (Hardcover)
  • All (8) from $29.69   
  • New (4) from $146.83   
  • Used (4) from $29.69   

Overview

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.

Read More Show Less

Editorial Reviews

From the Publisher

"It is well written, encyclopedic, and authoritative and probably belongs on the shelf of any commutative algebraist or algebraic number theorist."—MATHEMATICAL REVIEWS

Read More Show Less

Product Details

  • ISBN-13: 9780387985251
  • Publisher: Springer New York
  • Publication date: 5/21/1999
  • Series: Springer Monographs in Mathematics Series
  • Edition description: 1999
  • Edition number: 1
  • Pages: 403
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.00 (d)

Table of Contents

Preface
Notations
Introduction 1
Ch. 1 Absolute Values of Fields 3
Ch. 2 Valuations of a Field 55
Ch. 3 Polynomials and Henselian Valued Fields 79
Ch. 4 Extensions of Valuations 107
Ch. 5 Uniqueness of Extensions of Valuations and Poly-Complete Fields 127
Ch. 6 Extensions of Valuations: Numerical Relations 151
Ch. 7 Power Series and the Structure of Complete Valued Fields 185
Ch. 8 Decomposition and Inertia Theory 213
Ch. 9 Ramification Theory 227
Ch. 10 Valuation Characterizations of Dedekind Domains 263
Ch. 11 Galois Groups of Algebraic Extensions of Infinite Degree 307
Ch. 12 Ideals, Valuations, and Divisors in Algebraic Extensions of Infinite Degree over Q 333
Ch. 13 A Glimpse of Krull Valuations 365
App Commutative Fields and Characters of Finite Abelian Groups 373
Bibliography 391
Index 395
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)