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Table of contents (4 chapters)
Keywords
About this book
The book deals with the theory of valued fields and mutli-valued fields. The theory of Prüfer 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 Prüfer 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.
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)
Authors and Affiliations
Bibliographic Information
Book Title: Multi-Valued Fields
Authors: Yuri L. Ershov
Series Title: Siberian School of Algebra and Logic
DOI: https://doi.org/10.1007/978-1-4615-1307-0
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2001
Hardcover ISBN: 978-0-306-11068-9Published: 31 August 2001
Softcover ISBN: 978-1-4613-5489-5Published: 16 September 2012
eBook ISBN: 978-1-4615-1307-0Published: 11 November 2013
Edition Number: 1
Number of Pages: X, 270
Topics: Algebra, Field Theory and Polynomials, Commutative Rings and Algebras, Mathematical Logic and Foundations