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Siberian School of Algebra and Logic Ser.: Multi-Valued Fields by Yuri L. Ershov (2001, Hardcover)

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Title: Multi-Valued Fields. Language: English. Number of Pages: 270. Weight: 1.27 lbs. Publication Date: 2001-08-31. Publisher: Springer.

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Product Information

For more than 30 years, the author has studied the model-theoretic aspects of the theory of valued fields and multi-valued fields. Many of the key results included in this book were obtained by the author whilst preparing the manuscript. Thus the unique overview of the theory, as developed in the book, has been previously unavailable. The book deals with the theory of valued fields and mutli-valued fields. The theory of Pr fer rings is discussed from the geometric' point of view. The author shows that by introducing the Zariski topology on families of valuation rings, it is possible to distinguish two important subfamilies of Pr fer rings that correspond to Boolean and near Boolean families of valuation rings. Also, algebraic and model-theoretic properties of multi-valued fields with near Boolean families of valuation rings satisfying the local-global principle are studied. It is important that this principle is elementary, i.e., it can be expressed in the language of predicate calculus. The most important results obtained in the book include a criterion for the elementarity of an embedding of a multi-valued field and a criterion for the elementary equivalence for multi-valued fields from the class defined by the additional natural elementary conditions (absolute unramification, maximality and almost continuity of local elementary properties). The book concludes with a brief chapter discussing the bibliographic references available on the material presented, and a short history of the major developments within the field.

Product Identifiers

Publisher
Springer
ISBN-10
0306110687
ISBN-13
9780306110689
eBay Product ID (ePID)
1960072

Product Key Features

Author
Yuri L. Ershov
Publication Name
Multi-Valued Fields
Format
Hardcover
Language
English
Publication Year
2001
Series
Siberian School of Algebra and Logic Ser.
Type
Textbook
Number of Pages
X, 270 Pages

Dimensions

Item Length
9.3in
Item Width
6.1in
Item Weight
44.8 Oz

Additional Product Features

Number of Volumes
1 Vol.
Lc Classification Number
Qa150-272
Reviews
From the reviews:"The book is devoted to the investigation of fields with distinguished families of valuation rings. The author has been studying the model-theoretic aspects of the theory of valued fields and multi-valued fields for more than 30 years. Many of the key results included in the book are published for the first time. So, the unique overview of the theory presented in the book has been unavailable previously." (German Pestov, Zentralblatt MATH, Vol. 1073 (24), 2005), From the reviews: "The book is devoted to the investigation of fields with distinguished families of valuation rings. The author has been studying the model-theoretic aspects of the theory of valued fields and multi-valued fields for more than 30 years. Many of the key results included in the book are published for the first time. So, the unique overview of the theory presented in the book has been unavailable previously." (German Pestov, Zentralblatt MATH, Vol. 1073 (24), 2005)
Table of Content
1. Valuation Rings.- 1.1. Valuation Rings and Valuations of Fields.- 1.2. Valuation Rings in Algebraic Extensions.- 1.3. Henselian Valuation Rings.- 1.4. Alebgraic Extensions of Valued Fields.- 1.5. Immediate Extensions.- 1.6. Density.- 1.7. Constructions.- 2. Multi-Valued Fields.- 2.1. Prüfer Rings.- 2.2. The Zariski Topology and the Restriction Mapping.- 2.3. Affine Families of Valuation Rings.- 2.4. Weakly Boolean Families and Boolean Families of Valuation Rings.- 2.5. Near Boolean Families of Valuation Rings.- 2.6. Independence.- 3. Local-Global Properties of Near Boolean Families.- 3.1. Rational Points over Henselian Fields.- 3.2. Arithmetic Local-Global Principle.- 3.3. Equivalent Forms of Property LGA.- 3.4. Preservation of Property LGA under Algebraic Separable Extensions.- 3.5. Geometric Local-Global Principle.- 3.6. Existence of Families with Property LGA.- 4. Model-Theoretic Properties of Multi-Valued Fields.- 4.1. Embedding Theorems.- 4.2. The Robinson Theorem.- 4.3. Valued Fields.- 4.4. Finitely Multi-Valued Fields.- 4.5. Multi-Valued Fields with Boolean Families.- 4.6. Multi-Valued Fields with Near Boolean Families.- Bibliographical and Historical Remarks.- References.
Copyright Date
2001
Topic
Algebra / Abstract, Algebra / General, Number Theory, Logic
Lccn
2001-029947
Intended Audience
Scholarly & Professional
Illustrated
Yes
Genre
Mathematics

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Siberian School of Algebra and Logic Ser.: Multi-Valued Fields by Yuri L. Ershov (2001, Hardcover)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

All listings for this product

item 1 Multi-Valued Fields

item 2 Multi-Valued Fields by Yuri L. Ershov (English) Hardcover Book

Best Selling in Textbooks

Diagnostic and Statistical Manual of Mental Disorders DSM-5-TR by American Psychiatric Association (2022, Trade Paperback)

Leadership : Theory and Practice by Peter G. Northouse (2021, Trade Paperback, Revised edition)

Teaching Good Learner Repertoires by Steve Ward (2013, Trade Paperback)

Self Heal by Design : The Role of Micro-organisms for Health by Barbara O'Neill (2018, Trade Paperback)

Research Design : Qualitative, Quantitative, and Mixed Methods Approaches by J. David Creswell and John W. Creswell (2022, Trade Paperback)

Designing Data-Intensive Applications : The Big Ideas Behind Reliable, Scalable, and Maintainable Systems by Martin Kleppmann (2017, Trade Paperback)

Cognitive Behavior Therapy : Basics and Beyond by Judith S. Beck (2020, Hardcover)

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Diagnostic and Statistical Manual of Mental Disorders DSM-5-TR Brand new

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