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Author: Mike Prest
Publisher:
ISBN: 9781139649308
Category : MATHEMATICS
Languages : en
Pages : 798
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Book Description
A unified, coherent account of the algebraic aspects and uses of the Ziegler spectrum.
Author: Mike Prest
Publisher:
ISBN: 9781139649308
Category : MATHEMATICS
Languages : en
Pages : 798
Get Book
Book Description
A unified, coherent account of the algebraic aspects and uses of the Ziegler spectrum.
Author: Mike Prest
Publisher: Cambridge University Press
ISBN: 1139643894
Category : Mathematics
Languages : en
Pages : 798
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Book Description
It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches.
Author: Mike Prest
Publisher: American Mathematical Soc.
ISBN: 0821847678
Category : Mathematics
Languages : en
Pages : 122
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Book Description
Most of the model theory of modules works, with only minor modifications, in much more general additive contexts (such as functor categories, categories of comodules, categories of sheaves). Furthermore, even within a given category of modules, many subcategories form a ``self-sufficient'' context in which the model theory may be developed without reference to the larger category of modules. The notion of a definable additive category covers all these contexts. The (imaginaries) language which one uses for model theory in a definable additive category can be obtained from the category (of structures and homomorphisms) itself, namely, as the category of those functors to the category of abelian groups which commute with products and direct limits. Dually, the objects of the definable category--the modules (or functors, or comodules, or sheaves)--to which that model theory applies may be recovered as the exact functors from the, small abelian, category (the category of pp-imaginaries) which underlies that language.
Author: Graham J. Leuschke
Publisher: American Mathematical Soc.
ISBN: 1470435764
Category : Algebra
Languages : en
Pages : 296
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Book Description
This volume contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held from August 10-19, 2016, at Syracuse University, Syracuse, NY. Included are three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories. Other articles represent contributions to areas in and related to representation theory, such as noncommutative resolutions, twisted commutative algebras, and upper cluster algebras.
Author: Arthur James Wells
Publisher:
ISBN:
Category : Bibliography, National
Languages : en
Pages : 2744
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Book Description
Author: Henning Krause
Publisher: Cambridge University Press
ISBN: 1108985815
Category : Mathematics
Languages : en
Pages : 518
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Book Description
Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library.
Author: M. O. Manasreh
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 552
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Book Description
The MRS Symposium Proceeding series is an internationally recognised reference suitable for researchers and practitioners.
Author:
Publisher:
ISBN:
Category : Physics
Languages : en
Pages : 832
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Book Description
Author: Bruno Courcelle
Publisher: Cambridge University Press
ISBN: 1139644009
Category : Mathematics
Languages : en
Pages : 743
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Book Description
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
Author: Yves Crama
Publisher: Cambridge University Press
ISBN: 0521847524
Category : Computers
Languages : en
Pages : 781
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Book Description
A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.
