Model Theory and Modules Paperback: 130 (London Mathematical Society Lecture Note Series, Series Number 130) - Tapa blanda
Sinopsis
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.
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Acerca del autor
Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.
"Sobre este título" puede pertenecer a otra edición de este libro.
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Model Theory and Modules
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Cambridge University Press, 2008
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Condición: Good. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,800grams, ISBN:0521348331. Nº de ref. del artículo: 2936128
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LMS: 130 Model Theory and Modules (London Mathematical Society Lecture Note Series).
Publicado por
Cambridge University Press, 2008
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Broschur, Gr.-8°
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Broschur, Gr.-8°. Condición: Gut. 1. 380 S. Das Buch ist in gutem, sauberen Zustand. Einband berieben / fleckig. Ecken und Kanten leicht bestossen. Sonst sauberes und wohlerhaltenes Exemplar. -----Inhalt:. The interplay between model theory and other branches of mathematics has led to intriguing results. In this book, the theme is the interplay between model theory and the theory of modules. It is an introduction to the subject and introduces the requisite model theory and module theory as is needed.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. Introduction; Acknowledgements; Notations and conventions; Remarks on the development of the area; Section summaries; 1. Some preliminaries; 2. Positive primitive formulas and the sets they define; 3. Stability and totally transcendental modules; 4. Hulls; 5. Forking and ranks; 6. Stability-theoretic properties of types; 7. Superstable modules; 8. The lattice of pp-types and free realisations of pp-types; 9. Types and the structure of pure-injective modules; 10. Dimension and decomposition; 11. Modules over artinian rings; 12. Functor categories; 13. Modules over artin algebras; 14. Projective and flat modules; 15. Torsion and torsionfree classes; 16. Elimination of quantifiers; 17. Decidability and undecidability; Problems page; Bibliography; Examples index; Notation index; Index. ISBN: 9780521348331 Wir senden umgehend mit beiliegender MwSt.Rechnung. Sprache: Englisch Gewicht in Gramm: 590. Nº de ref. del artículo: 669015
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Model theory and modules / Mike Prest
Publicado por
Cambridge : Cambridge University Press, 1988
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Librería: MW Books Ltd., Galway, Irlanda
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First Edition. Very good paperback copy; edges slightly dust-dulled and nicked. Remains particularly well-preserved overall; tight, bright, and clean. Physical description: xviii, 380 pages; 21cm. Notes:Includes bibliographical references and indexes.Contents: Cover; Title; Copyright; Dedication; Preface; Contents; Introduction; Acknowledgements; Notations and conventions; Remarks on the development of the area; Section summaries; Chapter 1 Some preliminaries; 1.1 An introduction to model theory; 1.2 Injective modules and decomposition theorems; Chapter 2 Positive primitive formulas and the sets they define; 2.1 pp formulas; 2.2 pp-types; 2.3 Pure embeddings and pure-injective modules; 2.4 pp-elimination of quantifiers; 2.5 Immediate corollaries of pp-elimination of quantifiers; 2.6 Comparison of complete theories of modules2.Z pp formulas and types in abelian groups2.L Other languages; Chapter 3 Stability and totally transcendental modules; 3.1 Stability for modules; 3.2 A structure theorem for totally transcendental modules; part I; 3.A Abelian structures; Chapter 4 Hulls; 4.1 pp-essential embeddings and the construction of hulls; 4.2 Examples of hulls; 4.3 Decomposition of injective and pure-injective modules; 4.4 Irreducible types; 4.5 Limited and unlimited types; 4.6 A structure theory for totally transcendental modules; part II; 4.C Categoricity; 4.7 The space of indecomposablesChapter 5 Forking and ranks5.1 Forking and independence; 5.2 Ranks; 5.3 An algebraic characterisation of independence; 5.4 Independence when T = TXo; Chapter 6 Stability-theoretic properties of types; 6.1 Free parts of types and the stratified order; 6.2 Domination and the RK-order; 6.3 Orthogonality and the RK-order; 6.4 Regular types; 6.1 An example: injective modules over noetherian rings; 6.5 Saturation and pure-injective modules; 6.6 Multiplicity and strong types; Chapter 7 Superstable modules; 7.1 Superstable modules: the uncountable spectrum; 7.2 Modules of U-rank 1 7.3 Modules of finite U-rankChapter 8 The lattice of pp-types and free realisations of pp-types; 8.1 The lattice of pp-types; 8.2 Finitely generated pp-types; 8.3 pp-types and matrices; 8.4 Duality and pure-semisimple rings; Chapter 9 Types and the structure of pure-injective modules; 9.1 Minimal pairs; 9.2 Associated types; 9.3 Notions of isolation; 9.4 Neg-isolated types and elementary cogenerators; Chapter 10 Dimension and decomposition; 10.1 Existence of indecomposable direct summands; 10.2 Dimensions defined on lattices; 10.3 Modules with width 10.4 Classification for theories with dimension10.5 Krull dimension; 10.T Teq; 10.6 Dimension and height; 10.V Valuation rings; Chapter 11 Modules over artinian rings; 11.1 Pure-semisimple rings; 11.2 Pure-semisimple rings and rings of finite representation type; 11.3 Finite hulls over artinian rings; 11.4 Finite Morley rank and finite representation type; 11.P "Pathologies"; Chapter 12 Functor categories; 12.1 Functors defined from pp formulas; 12.2 Simple functors; 12.3 Embedding into functor categories; 12.P Pure global dimension and dimensions of functor categories Chapter 13 Modules over Artin algebrasSubjects: Model theory.Modules (Algebra)Model theory. Modules (Algebra) Model theory.Modules (Algebra)Théorie des modèles.Modules (Algèbre)Model theory. Modules (Algebra). Modèles, Théorie des. Modules (algèbre)MATHEMATICS General.Algebra Modules 1 Kg. Nº de ref. del artículo: 385362
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Model theory and modules / Mike Prest
Publicado por
Cambridge : Cambridge University Press, 1988
ISBN 10: 0521348331
ISBN 13: 9780521348331
Antiguo o usado
Tapa blanda
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Librería: MW Books, New York, NY, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
First Edition. Very good paperback copy; edges slightly dust-dulled and nicked. Remains particularly well-preserved overall; tight, bright, and clean. Physical description: xviii, 380 pages; 21cm. Notes:Includes bibliographical references and indexes.Contents: Cover; Title; Copyright; Dedication; Preface; Contents; Introduction; Acknowledgements; Notations and conventions; Remarks on the development of the area; Section summaries; Chapter 1 Some preliminaries; 1.1 An introduction to model theory; 1.2 Injective modules and decomposition theorems; Chapter 2 Positive primitive formulas and the sets they define; 2.1 pp formulas; 2.2 pp-types; 2.3 Pure embeddings and pure-injective modules; 2.4 pp-elimination of quantifiers; 2.5 Immediate corollaries of pp-elimination of quantifiers; 2.6 Comparison of complete theories of modules2.Z pp formulas and types in abelian groups2.L Other languages; Chapter 3 Stability and totally transcendental modules; 3.1 Stability for modules; 3.2 A structure theorem for totally transcendental modules; part I; 3.A Abelian structures; Chapter 4 Hulls; 4.1 pp-essential embeddings and the construction of hulls; 4.2 Examples of hulls; 4.3 Decomposition of injective and pure-injective modules; 4.4 Irreducible types; 4.5 Limited and unlimited types; 4.6 A structure theory for totally transcendental modules; part II; 4.C Categoricity; 4.7 The space of indecomposablesChapter 5 Forking and ranks5.1 Forking and independence; 5.2 Ranks; 5.3 An algebraic characterisation of independence; 5.4 Independence when T = TXo; Chapter 6 Stability-theoretic properties of types; 6.1 Free parts of types and the stratified order; 6.2 Domination and the RK-order; 6.3 Orthogonality and the RK-order; 6.4 Regular types; 6.1 An example: injective modules over noetherian rings; 6.5 Saturation and pure-injective modules; 6.6 Multiplicity and strong types; Chapter 7 Superstable modules; 7.1 Superstable modules: the uncountable spectrum; 7.2 Modules of U-rank 1 7.3 Modules of finite U-rankChapter 8 The lattice of pp-types and free realisations of pp-types; 8.1 The lattice of pp-types; 8.2 Finitely generated pp-types; 8.3 pp-types and matrices; 8.4 Duality and pure-semisimple rings; Chapter 9 Types and the structure of pure-injective modules; 9.1 Minimal pairs; 9.2 Associated types; 9.3 Notions of isolation; 9.4 Neg-isolated types and elementary cogenerators; Chapter 10 Dimension and decomposition; 10.1 Existence of indecomposable direct summands; 10.2 Dimensions defined on lattices; 10.3 Modules with width 10.4 Classification for theories with dimension10.5 Krull dimension; 10.T Teq; 10.6 Dimension and height; 10.V Valuation rings; Chapter 11 Modules over artinian rings; 11.1 Pure-semisimple rings; 11.2 Pure-semisimple rings and rings of finite representation type; 11.3 Finite hulls over artinian rings; 11.4 Finite Morley rank and finite representation type; 11.P "Pathologies"; Chapter 12 Functor categories; 12.1 Functors defined from pp formulas; 12.2 Simple functors; 12.3 Embedding into functor categories; 12.P Pure global dimension and dimensions of functor categories Chapter 13 Modules over Artin algebrasSubjects: Model theory.Modules (Algebra)Model theory. Modules (Algebra) Model theory.Modules (Algebra)Théorie des modèles.Modules (Algèbre)Model theory. Modules (Algebra). Modèles, Théorie des. Modules (algèbre)MATHEMATICS General.Algebra Modules 1 Kg. Nº de ref. del artículo: 385362
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LMS: 130 Model Theory and Modules (London Mathematical Society Lecture Note Series)
Publicado por
Cambridge University Press, 1988
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Paperback
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Paperback. Condición: Good. Type: Book N.B. Small plain label to inside front cover. Corners of covers a little rubbed. Nº de ref. del artículo: 054652
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Model theory and modules Mike Prest. Lecture note series 130.
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Cambridge, Cambridge University Press, 1988
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Softcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 13 PRE 9780521348331 Sprache: Englisch Gewicht in Gramm: 1150. Nº de ref. del artículo: 2504059
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Model theory and modules Mike Prest. Lecture note series 130.
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Cambridge New York , Cambridge University Press, 1988
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Softcover
Librería: Antiquariat Bookfarm, Löbnitz, Alemania
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Softcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 13 PRE 9780521348331 Sprache: Englisch Gewicht in Gramm: 1150. Nº de ref. del artículo: 2499213
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Model Theory and Modules (London Mathematical Society Lecture Note Series, Series Number 130)
Publicado por
Cambridge University Press, 1988
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Model Theory and Modules
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Cambridge University Press, 1988
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Model Theory and Modules (Paperback)
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Cambridge University Press, Cambridge, 1988
ISBN 10: 0521348331
ISBN 13: 9780521348331
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Paperback. Condición: new. Paperback. Professor Prest is the first to address the topic of the development of the interplay between model theory and the theory of modules. In recent years the relationship between model theory and other branches of mathematics has led to many profound and intriguing results. This self-contained introduction to the subject introduces the requisite model theory and module theory as it is needed. It then develops the basic ideas of determining what can be said about modules using the information that may be expressed in 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. Professor Prest is the first to address the topic of the development of the interplay between model theory and the theory of modules. In recent years the relationship between model theory and other branches of mathematics has led to many profound and intriguing results. This self-contained introduction to the subject introduces the requisite model theory and module theory as it is needed. It then develops the basic ideas of determining what can be said about modules using the information that may be expressed in 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9780521348331
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