Model Theory Of Modules Algebras And Categories

Author : Alberto Facchini
Publisher : American Mathematical Soc.
ISBN 13 : 1470443678
Total Pages : 237 pages
Book Rating : 4.72/5 ( download)

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Download or read book Model Theory of Modules, Algebras and Categories written by Alberto Facchini and published by American Mathematical Soc.. This book was released on 2019-05-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Mike Prest
Publisher : Cambridge University Press
ISBN 13 : 0521348331
Total Pages : 402 pages
Book Rating : 4.31/5 ( download)

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Download or read book Model Theory and Modules written by Mike Prest and published by Cambridge University Press. This book was released on 1988-02-25 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : M Droste
Publisher : CRC Press
ISBN 13 : 1000717453
Total Pages : 512 pages
Book Rating : 4.57/5 ( download)

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Download or read book Advances in Algebra and Model Theory written by M Droste and published by CRC Press. This book was released on 2019-08-16 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.

Author : Mark Hovey
Publisher : American Mathematical Soc.
ISBN 13 : 0821843613
Total Pages : 229 pages
Book Rating : 4.11/5 ( download)

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Download or read book Model Categories written by Mark Hovey and published by American Mathematical Soc.. This book was released on 2007 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Carl Faith
Publisher : Springer Science & Business Media
ISBN 13 : 3642806341
Total Pages : 589 pages
Book Rating : 4.46/5 ( download)

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Download or read book Algebra written by Carl Faith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: VI of Oregon lectures in 1962, Bass gave simplified proofs of a number of "Morita Theorems", incorporating ideas of Chase and Schanuel. One of the Morita theorems characterizes when there is an equivalence of categories mod-A R::! mod-B for two rings A and B. Morita's solution organizes ideas so efficiently that the classical Wedderburn-Artin theorem is a simple consequence, and moreover, a similarity class [AJ in the Brauer group Br(k) of Azumaya algebras over a commutative ring k consists of all algebras B such that the corresponding categories mod-A and mod-B consisting of k-linear morphisms are equivalent by a k-linear functor. (For fields, Br(k) consists of similarity classes of simple central algebras, and for arbitrary commutative k, this is subsumed under the Azumaya [51]1 and Auslander-Goldman [60J Brauer group. ) Numerous other instances of a wedding of ring theory and category (albeit a shot gun wedding!) are contained in the text. Furthermore, in. my attempt to further simplify proofs, notably to eliminate the need for tensor products in Bass's exposition, I uncovered a vein of ideas and new theorems lying wholely within ring theory. This constitutes much of Chapter 4 -the Morita theorem is Theorem 4. 29-and the basis for it is a corre spondence theorem for projective modules (Theorem 4. 7) suggested by the Morita context. As a by-product, this provides foundation for a rather complete theory of simple Noetherian rings-but more about this in the introduction.

Author : Alexander Martsinkovsky
Publisher : Springer Nature
ISBN 13 : 3031530632
Total Pages : 256 pages
Book Rating : 4.30/5 ( download)

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Download or read book Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods written by Alexander Martsinkovsky and published by Springer Nature. This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Anthony D. Elmendorf
Publisher : American Mathematical Soc.
ISBN 13 : 0821843036
Total Pages : 265 pages
Book Rating : 4.31/5 ( download)

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Download or read book Rings, Modules, and Algebras in Stable Homotopy Theory written by Anthony D. Elmendorf and published by American Mathematical Soc.. This book was released on 1997 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ``$S$-modules'' whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ``$S$-algebras'' and ``commutative $S$-algebras'' in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a

Author : Frank W. Anderson
Publisher : Springer Science & Business Media
ISBN 13 : 1461244188
Total Pages : 386 pages
Book Rating : 4.89/5 ( download)

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Download or read book Rings and Categories of Modules written by Frank W. Anderson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.

Author : Christian.U Jensen
Publisher : Routledge
ISBN 13 : 1351431129
Total Pages : 464 pages
Book Rating : 4.25/5 ( download)

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Download or read book Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules written by Christian.U Jensen and published by Routledge. This book was released on 2022-03-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alex Heller
Publisher : Academic Press
ISBN 13 : 1483262618
Total Pages : 238 pages
Book Rating : 4.11/5 ( download)

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Download or read book Algebra, Topology, and Category Theory written by Alex Heller and published by Academic Press. This book was released on 2014-05-10 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra, Topology, and Category Theory: A Collection of Papers in Honor of Samuel Eilenberg is a collection of papers dealing with algebra, topology, and category theory in honor of Samuel Eilenberg. Topics covered range from large modules over artin algebras to two-dimensional Poincaré duality groups, along with the homology of certain H-spaces as group ring objects. Variable quantities and variable structures in topoi are also discussed. Comprised of 16 chapters, this book begins by looking at the relationship between the representation theories of finitely generated and large (not finitely generated) modules over an artin algebra. The reader is then introduced to reduced bar constructions on deRham complexes; some properties of two-dimensional Poincaré duality groups; and properties invariant within equivalence types of categories. Subsequent chapters explore the work of Samuel Eilenberg in topology; local complexity of finite semigroups; global dimension of ore extensions; and the spectrum of a ringed topos. This monograph will be a useful resource for students and practitioners of algebra and mathematics.