Model Theory And Modules
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Model Theory And Modules
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Author : Mike Prest
language : en
Publisher: Cambridge University Press
Release Date : 1988-02-25
Model Theory And Modules written by Mike Prest 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 1988-02-25 with Mathematics categories.
In recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules. Both algebraists and logicians will enjoy this account of an area in which algebra and model theory interact in a significant way. The book includes numerous examples and exercises and consequently will make an ideal introduction for graduate students coming to this subject for the first time.
Model Theory Of Modules Algebras And Categories
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Author : Alberto Facchini
language : en
Publisher:
Release Date : 1929
Model Theory Of Modules Algebras And Categories written by Alberto Facchini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1929 with Algebra categories.
This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28-August 2, 2017, at the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, Italy. Papers contained in this volume cover recent developments in model theory, module theory and category theory, and their intersection.
Model Theoretic Algebra With Particular Emphasis On Fields Rings Modules
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Author : Christian. U Jensen
language : en
Publisher: CRC Press
Release Date : 1989-07-26
Model Theoretic Algebra With Particular Emphasis On Fields Rings Modules written by Christian. U Jensen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-26 with Mathematics categories.
Looks like a text (and a handsome one at that), but the authors prefer to describe their creation as "notes", intended to acquaint graduate students with "the power of the most basic principles of model theory by applying them to classical questions in algebra". Thirteen chapters (the last given to the enumeration of some open problems), plus tables and several appendices, bibliography. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
D Modules Perverse Sheaves And Representation Theory
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Author : Ryoshi Hotta
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-07
D Modules Perverse Sheaves And Representation Theory written by Ryoshi Hotta 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 2007-11-07 with Mathematics categories.
D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
A Shorter Model Theory
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Author : Wilfrid Hodges
language : en
Publisher: Cambridge University Press
Release Date : 1997-04-10
A Shorter Model Theory written by Wilfrid Hodges 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 1997-04-10 with Mathematics categories.
This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
Introduction To Model Theory
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Author : Philipp Rothmaler
language : en
Publisher: CRC Press
Release Date : 2018-12-07
Introduction To Model Theory written by Philipp Rothmaler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.
Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
Model Theory
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Author : Wilfrid Hodges
language : en
Publisher: Cambridge University Press
Release Date : 2008-06-19
Model Theory written by Wilfrid Hodges 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 2008-06-19 with Mathematics categories.
Professor Hodges emphasizes definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference.
Foundations Of Module And Ring Theory
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Author : Robert Wisbauer
language : en
Publisher: Routledge
Release Date : 2018-05-11
Foundations Of Module And Ring Theory written by Robert Wisbauer and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.
This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
Models Logics And Higher Dimensional Categories
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Author : Bradd T. Hart
language : en
Publisher: American Mathematical Soc.
Release Date :
Models Logics And Higher Dimensional Categories written by Bradd T. Hart 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 with Mathematics categories.
Proceedings of a conference held at Centre de recherches mathematiques of the Universite de Montreal, June 18-20, 2009.
Model Theory And Applications
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Author : O.V. Belegradek
language : en
Publisher: American Mathematical Soc.
Release Date :
Model Theory And Applications written by O.V. Belegradek 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 with Mathematics categories.
This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists. The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.