Infinite Length Modules

by Krause, Henning; Ringel, Claus Michael

• ISBN13: 9783764364137
• ISBN10: 3764364130
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-12-01
• Publisher: Springer Verlag

Summary

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

Preface	vii
Infinite length modules. Some Examples as Introduction	1	(74)
C.M. Ringel
Modules with strange decomposition properties	75	(14)
P.C. Eklof
Failure of the Krull-Schmidt theorem for artinian modules and serial modules	89	(12)
A. Facchini
Artinian modules over a matrix ring	101	(6)
K.I. Pimenov
A.V. Yakovlev
Some combinatorial principles for solving algebriac problems	107	(22)
R. Gobel
Dimension theory of noetherian rings	129	(20)
T.H. Lenagan
Krull, Gelfand-Kirillov, Filter, Faithful and Schur dimensions	149	(18)
V. Bavula
Cohen-Macaulay modules and approximations	167	(26)
A. Martsinkovsky
The generic representation theory of finite fields. A survey of basic structures	193	(20)
N.J. Kuhn
On artinian objects in the category of functors between F2-vector spaces	213	(16)
G.M.L. Powell
Unstable modules over the Steenrod algebra, functors, and the cohomology of spaces	229	(22)
L. Schwartz
Infinite dimensional modules for finite groups	251	(22)
D.J. Benson
Bousfield localization for representation theoretists	273	(12)
J. Rickard
The thick subcategory generated by the trivial module	285	(12)
J.F. Carlson
Birational classification of moduli spaces	297	(14)
A. Schofield
Tame algebras and degenerations of modules	311	(10)
G. Zwara
On some tame and discrete families of modules	321	(10)
R. Bautista
Purity, algebraic compactness, direct sum decompositions, and representation type	331	(38)
B. Huisgen-Zimmermann
Topological and geometrical aspects of the Ziegler spectrum	369	(24)
M. Prest
Finite versus infinite dimensional representations. A new definition of tameness	393	(12)
H. Krause
Invariance of tameness under stable equivalence: Krause's theorem	405	(14)
H. Lenzing
The Krull-Gabriel dimension of an algebra. Open problems and conjectures	419	(6)
J. Schroer
Homological differences between finite and infinite dimensional representations of algebras	425
S.O. Smalø