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Mathematical Surveys and Monographs
Volume: 124; 2006; 288 pp; Hardcover
MSC: Primary 12; Secondary 19

Print ISBN: 978-0-8218-4041-2
Product Code: SURV/124
List Price: $86.00
AMS Member Price: $68.80
MAA Member Price: $77.40

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Electronic ISBN: 978-1-4704-1351-4
Product Code: SURV/124.E
List Price: $81.00
AMS Member Price: $64.80
MAA Member Price: $72.90

Supplemental Materials

Valuations, Orderings, and Milnor $K$-Theory

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Ido Efrat

This monograph is a comprehensive exposition of the modern theory of valued and ordered fields. It presents the classical aspects of such fields: their arithmetic, topology, and Galois theory. Deeper cohomological aspects are studied in its last part in an elementary manner. This is done by means of the newly developed theory of generalized Milnor $K$-rings. The book emphasizes the close connections and interplay between valuations and orderings, and to a large extent, studies them in a unified manner.

The presentation is almost entirely self-contained. In particular, the text develops the needed machinery of ordered abelian groups. This is then used throughout the text to replace the more classical techniques of commutative algebra. Likewise, the book provides an introduction to the Milnor $K$-theory.

The reader is introduced to the valuation-theoretic techniques as used in modern Galois theory, especially in applications to birational anabelian geometry, where one needs to detect valuations from their “cohomological footprints”. These powerful techniques are presented here for the first time in a unified and elementary way.

Readership

Graduate students and research mathematicians interested in valuations and orderings on fields (algebra and number theory).

Reviews & Endorsements

This book provides a thorough and well-presented introduction to the valuations and orderings on a field, and developsa formalism of relative higher Milnor $K$-theory of fields.

-- Mathematical Reviews

Valuations, Orderings, and Milnor $K$-Theory

Base Product Code Keyword List: surv; SURV; surv/124; SURV/124; surv-124; SURV-124

Print Product Code: SURV/124

Online Product Code: SURV/124.E

Title (HTML): Valuations, Orderings, and Milnor $K$-Theory

Author(s) (Product display): Ido Efrat

Affiliation(s) (HTML): Ben-Gurion University of the Negev, Be’er-Sheva, Israel

Abstract:

Book Series Name: Mathematical Surveys and Monographs

Volume: 124

Publication Month and Year: 2006-03-28

Page Count: 288

Cover Type: Hardcover

Print ISBN-13: 978-0-8218-4041-2

Online ISBN 13: 978-1-4704-1351-4

Print ISSN: 0076-5376

Online ISSN: 0076-5376

Primary MSC: 12

Secondary MSC: 19

Textbook?: false

Applied Math?: false

MAA Book?: false

Inquiry Based Learning?: false

Electronic Media?: false

Apparel or Gift: false

SXG Subject: NT

Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/surv-124

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Online Price 1: 81.00

Print Price 1 Label: List

Print Price 1: 86.00

Online Price 2 Label: AMS Member

Online Price 2: 64.80

Print Price 2 Label: AMS Member

Print Price 2: 68.80

Online Price 3 Label: MAA Member

Online Price 3: 72.90

Print Price 3 Label: MAA Member

Print Price 3: 77.40

Bundle Price 1 Label: List

Bundlel Price 1: 126.50

Bundle Price 2 Label: AMS Member

Bundle Price 2: 101.20

Bundle Price 3: 113.85

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Print Add to Cart URL: /some/url/at/AMS/SURV-124

Electronic Add to Cart URL: /some/url/at/AMS/SURV-124.E

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Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1351-4&pisbn=978-0-8218-4041-2&epc=SURV/124.E&ppc=SURV/124&title=Valuations%2C%20Orderings%2C%20and%20Milnor%20%24K%24-Theory&author=Ido%20Efrat&type=R

Readership:

Graduate students and research mathematicians interested in valuations and orderings on fields (algebra and number theory).

Reviews:

This book provides a thorough and well-presented introduction to the valuations and orderings on a field, and developsa formalism of relative higher Milnor $K$-theory of fields.

-- Mathematical Reviews

CCC Permissions Link: https://www.copyright.com/openurl.do?isbn=9780821840412&WT.mc.id=American%20Mathematical%20Society

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Contents
- Contents
Introduction
- Introduction
Conventions
- Conventions
Part I. Abelian Groups
- Part I. Abelian Groups
Index
- Index

Supplemental Materials

Valuations, Orderings, and Milnor \(K\)-Theory

Readership

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Table of Contents

Valuations, Orderings, and Milnor $K$-Theory

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Contents

Introduction

Conventions

Part I. Abelian Groups

Index