Infinite Length Modules (ICRA 8.5, Bielefeld 1998)

✍ Scribed by Henning Krause, Claus M. Ringel (editors)

• Publisher: Birkhäuser Basel
• Year: 2000
• Tongue: English
• Leaves: 447
• Edition: 1
• Category: Library

✦ Synopsis

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.The volume presents the invited lectures of a conference devoted to "Infinite Length Modules", held at Bielefeld in September 1998, which brought together experts from quite different schools in order to survey surprising relations between algebra, topology and geometry. Some additional reports have been included in order to establish a unified picture. The collection of articles, written by well-known experts from all parts of the world, is conceived as a sort of handbook which provides an easy access to the present state of knowledge and its aim is to stimulate further development.

✦ Table of Contents

Infinite Length Modules......Page 1
Contents......Page 3
Preface......Page 5
Ringel: Infinite length modules. Some examples as introduction......Page 9
Eklof: Modules with strange decomposition properties......Page 83
Facchini: Failure of the Krull-Schmidt Theorem for Artinian modules and serial modules......Page 97
Pimenov and Yakovlev: Artinian modules over a matrix ring......Page 109
Göbel: Some combinatorial principles for solving algebraic problems......Page 115
Lenagan: Dimension theory of Noetherian rings......Page 137
Bavula: Krull, Gelfand-Kirillov, filter, faithful and Schur dimensions......Page 157
Martsinkovsky: Cohen-Macaulay modules and approximations......Page 175
Kuhn: The generic representation theory of finite fields: a survey of basic structure......Page 201
Powell: On Artinian objects in the category of functors between F2-vector spaces......Page 221
Schwartz: Unstable modules over the Steenrod algebra, functors, and the cohomology of spaces......Page 237
Benson: Infinite dimensional modules for finite groups......Page 259
Rickard: Bousfield localization for representation theorists......Page 281
Carlson: The thick subcategory generated by the trivial module......Page 293
Schofield: Birational classification of moduli spaces......Page 305
Zwara: Tame algebras and degenerations of modules......Page 319
Bautista: On some tame and discrete families of modules......Page 329
Huisgen-Zimmermann: Purity, algebraic compactness, direct sum decompositions, and representation type......Page 339
Prest: Topological and geometric aspects of the Ziegler spectrum......Page 377
Krause: Finite versus infinite dimensional representations - a new definition of tameness......Page 401
Lenzing: Invariance of tameness under stable equivalence: Krause's theorem......Page 413
Schröer: The Krull-Gabriel dimension of an algebra - open problems and conjectures......Page 427
Smalø: Homological differences between finite and infinite dimensional representations of algebras......Page 433