Model Theory And Modules
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| Author | : Mike Prest |
| Publisher | : Cambridge University Press |
| Total Pages | : 402 |
| Release | : 1988-02-25 |
| Genre | : Mathematics |
| ISBN | : 0521348331 |
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.
| Author | : Christian.U Jensen |
| Publisher | : Routledge |
| Total Pages | : 458 |
| Release | : 2022-03-10 |
| Genre | : Mathematics |
| ISBN | : 1351431129 |
This volume highlights the links between model theory and algebra. The work contains a definitive account of algebraically compact modules, a topic of central importance for both module and model theory. Using concrete examples, particular emphasis is given to model theoretic concepts, such as axiomizability. Pure mathematicians, especially algebraists, ring theorists, logicians, model theorists and representation theorists, should find this an absorbing and stimulating book.
| Author | : Alberto Facchini |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 2019-05-31 |
| Genre | : Mathematics |
| ISBN | : 1470443678 |
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.
| Author | : Wilfrid Hodges |
| Publisher | : Cambridge University Press |
| Total Pages | : 810 |
| Release | : 1993-03-11 |
| Genre | : Mathematics |
| ISBN | : 9780521304429 |
Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.
| Author | : Alberto Facchini |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2012-02-03 |
| Genre | : Mathematics |
| ISBN | : 3034803036 |
This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.
| Author | : Mark Hovey |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 229 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821843613 |
Model categories are used as a tool for inverting certain maps in a category in a controllable manner. They are useful in diverse areas of mathematics. This book offers a comprehensive study of the relationship between a model category and its homotopy category. It develops the theory of model categories, giving a development of the main examples.
| Author | : Alex Martsinkovsky |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 216 |
| Release | : 2018-09-12 |
| Genre | : Mathematics |
| ISBN | : 1470436795 |
This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.
| Author | : Idun Reiten |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 216 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9780821808504 |
Surveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR
| Author | : John T. Baldwin |
| Publisher | : Cambridge University Press |
| Total Pages | : 463 |
| Release | : 2017-03-02 |
| Genre | : Mathematics |
| ISBN | : 1316739341 |
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the twelfth publication in the Perspectives in Logic series, John T. Baldwin presents an introduction to first order stability theory, organized around the spectrum problem: calculate the number of models a first order theory T has in each uncountable cardinal. The author first lays the groundwork and then moves on to three sections: independence, dependence and prime models, and local dimension theory. The final section returns to the spectrum problem, presenting complete proofs of the Vaught conjecture for ω-stable theories for the first time in book form. The book provides much-needed examples, and emphasizes the connections between abstract stability theory and module theory.
| Author | : Henning Krause |
| Publisher | : Birkhäuser |
| Total Pages | : 437 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034884265 |
This book is concerned with the role played by modules of infinite length when dealing with problems in the representation theory of groups and algebras, but also in topology and geometry; it shows the intriguing interplay between finite and infinite length modules.
