Continuous and Discrete Modules

Front Cover
Cambridge University Press, Feb 22, 1990 - Mathematics - 126 pages
Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory.
 

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Contents

Injectivity and related concepts
1
Quasicontinuous modules
18
Continuous modules
39
Quasidiscrete modules
55
Discrete modules
81
Appendix
95
18
107
Bibliography
108
46
114
62
120
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