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Book Cover
E-book
Author Mohamed, Saad H

Title Continuous and discrete modules / Saad H. Mohamed, Bruno J. Müller
Published Cambridge ; New York : Cambridge University Press, 1990

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Description 1 online resource (126 pages)
Series London Mathematical Society lecture note series ; 147
London Mathematical Society lecture note series ; 147.
Contents Cover; Title; Copyright; Preface; Contents; Chapter 1: Injectivity and related concepts; 1.A-injective modules; 2. Quasi-injective modules; 3. Exchange and cancellation properties; 4. Decomposition theorems; Comments; Chapter 2: Quasi-continuous modules; 1. Basic properties; 2. Direct sums of quasi-continuous modules; 3. Decompositions of quasi-continuous modules; 4. Internal cancellation property; 5. Quasi-continuity versus quasi-injectivity; Comments; Chapter 3: Continuous modules; 1. Endomorphism rings; 2. Continuous modules; 3. The exchange property; Comments; Chapter 4: Quasi-discrete modules
1. Definition and basic results2. Decomposition theorems; 3. Applications of the decomposition theorems; 4. Discreteness and projectivity; 5. Quasi-discreteness of direct sums; Comments; Chapter 5: Discrete modules; 1. Discrete modules; 2. Endomorphism rings; 3.Commutative noetherian rings; Comments; Appendix; 1. Variants of supplementation; 2. Supplements are summands; 3. Extending modules; 4. The historial origin of the concept of; 5.N -continuity; 6. Open questions; Bibliography; Notation; Index
Summary 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
Bibliography Includes bibliographical references (pages 108-121) and index
Notes Print version record
Subject Injective modules (Algebra)
Projective modules (Algebra)
Representations of rings (Algebra)
Decomposition (Mathematics)
MATHEMATICS -- Algebra -- Intermediate.
Decomposition (Mathematics)
Injective modules (Algebra)
Projective modules (Algebra)
Representations of rings (Algebra)
Stetiger Modul
Diskreter Modul
Modules (Algèbre)
Form Electronic book
Author Müller, Bruno J
ISBN 9781107361669
1107361664
9780511892523
0511892527