Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
Infinite length modules. Some Examples as Introduction.- Modules with strange decomposition properties.- Failure of the Krull-Schmidt theorem for artinian modules and serial modules.- Artinian modules over a matrix ring.- Some combinatorial principles for solving algebraic problems.- Dimension theory of noetherian rings.- Krull, Gelfand-Kirillov, Filter, Faithful and Schur dimensions.- Cohen-Macaulay modules and approximations.- The generic representation theory of finite fields A survey of basic structures.- On artinian objects in the category of functors between $${{\mathbb{F}}_{2}} $$ -vector spaces.- Unstable modules over the Steenrod algebra, functors, and the cohomology of spaces.- Infinite dimensional modules for finite groups.- Bousfield localization for representation theoretists.- The thick subcategory generated by the trivial module.- Birational classification of moduli spaces.- Tame algebras and degenerations of modules.- On some tame and discrete families of modules.- Purity, algebraic compactness, direct sum decompositions, and representation type.- Topological and geometrical aspects of the Ziegler spectrum.- Finite versus infinite dimensional representations A new definition of tameness.- Invariance of tameness under stable equivalence:Krause’s theorem.- The Krull-Gabriel dimension of an algebra Open problems and conjectures.- Homological differences between finite and infinite dimensional representations of algebras.
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Infinite Length Modules (eng)
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Infinite Length Modules (Trends in Mathematics)
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Infinite Length Modules
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 452 pp. Englisch. Codice articolo 9783034895620
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 len. Codice articolo 4319375
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This volume presents the invited lectures of a conference devoted to Infinite Length Modules, held at Bielefeld, September 7-11, 1998. Some additional surveys have been included in order to establish a unified picture. The scientific organization of the conference was in the hands of K. Brown (Glasgow), P. M. Cohn (London), I. Reiten (Trondheim) and C. M. Ringel (Bielefeld). The conference was concerned with the role played by modules of infinite length when dealing with problems in the representation theory of algebras. The investi gation of such modules always relies on information concerning modules of finite length, for example simple modules and their possible extensions. But the converse is also true: recent developments in representation theory indicate that a full un derstanding of the category of finite dimensional modules, even over a finite dimen sional algebra, requires consideration of infinite dimensional, thus infinite length, modules. For instance, the important notion of tameness uses one-parameter fami lies of modules, or, alternatively, generic modules and they are of infinite length. If one tries to exhibit a presentation of a module category, it turns out to be essential to take into account the indecomposable modules which are algebraically compact, or, equivalently, pure injective. Specific methods have been developed over the last few years dealing with such special situations as group algebras of finite groups or noetherian rings, and there are surprising relations to topology and geometry. The conference outlined the present state of the art.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 452 pp. Englisch. Codice articolo 9783034895620
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This volume presents the invited lectures of a conference devoted to Infinite Length Modules, held at Bielefeld, September 7-11, 1998. Some additional surveys have been included in order to establish a unified picture. The scientific organization of the conference was in the hands of K. Brown (Glasgow), P. M. Cohn (London), I. Reiten (Trondheim) and C. M. Ringel (Bielefeld). The conference was concerned with the role played by modules of infinite length when dealing with problems in the representation theory of algebras. The investi gation of such modules always relies on information concerning modules of finite length, for example simple modules and their possible extensions. But the converse is also true: recent developments in representation theory indicate that a full un derstanding of the category of finite dimensional modules, even over a finite dimen sional algebra, requires consideration of infinite dimensional, thus infinite length, modules. For instance, the important notion of tameness uses one-parameter fami lies of modules, or, alternatively, generic modules and they are of infinite length. If one tries to exhibit a presentation of a module category, it turns out to be essential to take into account the indecomposable modules which are algebraically compact, or, equivalently, pure injective. Specific methods have been developed over the last few years dealing with such special situations as group algebras of finite groups or noetherian rings, and there are surprising relations to topology and geometry. The conference outlined the present state of the art. Codice articolo 9783034895620
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Taschenbuch. Condizione: Neu. Infinite Length Modules | Henning Krause (u. a.) | Taschenbuch | ix | Englisch | 2012 | Birkhäuser | EAN 9783034895620 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Codice articolo 105706220
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