Valued Fields
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Valued Fields
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Author : Antonio J. Engler
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-28
Valued Fields written by Antonio J. Engler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-28 with Mathematics categories.
Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.
Multi Valued Fields
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Author : Yuri L. Ershov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-31
Multi Valued Fields written by Yuri L. Ershov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-31 with Mathematics categories.
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 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.
Multi Valued Fields
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Author : Yuri L. Ershov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Multi Valued Fields written by Yuri L. Ershov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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 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.
Stable Domination And Independence In Algebraically Closed Valued Fields
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Author : Deirdre Haskell
language : en
Publisher: Cambridge University Press
Release Date : 2008
Stable Domination And Independence In Algebraically Closed Valued Fields written by Deirdre Haskell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book presents research in model theory and its applications to valued fields.
Sequence Spaces And Summability Over Valued Fields
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Author : P. N. Natarajan
language : en
Publisher: CRC Press
Release Date : 2019-07-09
Sequence Spaces And Summability Over Valued Fields written by P. N. Natarajan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-09 with Mathematics categories.
Sequence spaces and summability over valued fields is a research book aimed at research scholars, graduate students and teachers with an interest in Summability Theory both Classical (Archimedean) and Ultrametric (non-Archimedean). The book presents theory and methods in the chosen topic, spread over 8 chapters that seem to be important at research level in a still developing topic. Key Features Presented in a self-contained manner Provides examples and counterexamples in the relevant contexts Provides extensive references at the end of each chapter to enable the reader to do further research in the topic Presented in the same book, a comparative study of Archimedean and non-Archimedean Summability Theory Appeals to young researchers and experienced mathematicians who wish to explore new areas in Summability Theory The book is written by a very experienced educator and researcher in Mathematical Analysis particularly Summability Theory.
Bounds On Transfer Principles For Algebraically Closed And Complete Discretely Valued Fields
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Author : Scott Shorey Brown
language : en
Publisher: American Mathematical Soc.
Release Date : 1978
Bounds On Transfer Principles For Algebraically Closed And Complete Discretely Valued Fields written by Scott Shorey Brown and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Sequence Spaces And Summability Over Valued Fields
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Author : P. N. Natarajan
language : en
Publisher: CRC Press
Release Date : 2019-07-09
Sequence Spaces And Summability Over Valued Fields written by P. N. Natarajan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-09 with Mathematics categories.
Sequence spaces and summability over valued fields is a research book aimed at research scholars, graduate students and teachers with an interest in Summability Theory both Classical (Archimedean) and Ultrametric (non-Archimedean). The book presents theory and methods in the chosen topic, spread over 8 chapters that seem to be important at research level in a still developing topic. Key Features Presented in a self-contained manner Provides examples and counterexamples in the relevant contexts Provides extensive references at the end of each chapter to enable the reader to do further research in the topic Presented in the same book, a comparative study of Archimedean and non-Archimedean Summability Theory Appeals to young researchers and experienced mathematicians who wish to explore new areas in Summability Theory The book is written by a very experienced educator and researcher in Mathematical Analysis particularly Summability Theory.
Topological Fields And Near Valuations
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Author : Niel Shell
language : en
Publisher: CRC Press
Release Date : 2021-06-23
Topological Fields And Near Valuations written by Niel Shell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-23 with Mathematics categories.
Part I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory.
Valuation Theory In Interaction
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Author :
language : en
Publisher:
Release Date : 2014
Valuation Theory In Interaction written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Valuations Of Skew Fields And Projective Hjelmslev Spaces
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Author : Karl Mathiak
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1986-03
Valuations Of Skew Fields And Projective Hjelmslev Spaces written by Karl Mathiak and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-03 with Mathematics categories.