Continuous and discrete modules / Saad H. Mohamed, Bruno J. Müller.

Format:

Book

Author/Creator:

Mohamed, Saad H., author.

Müller, Bruno J., author.

Series:

London Mathematical Society lecture note series ; 147.

London Mathematical Society lecture note series ; 147

Language:

English

Subjects (All):

Injective modules (Algebra).

Projective modules (Algebra).

Representations of rings (Algebra).

Decomposition (Mathematics).

Physical Description:

1 online resource (126 pages) : digital, PDF file(s).

Other Title:

Continuous & Discrete Modules

Place of Publication:

Cambridge : Cambridge University Press, 1990.

Language Note:

English

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.

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

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. [108]-121) and index.

ISBN:

1-139-88461-1

1-107-36657-7

1-107-37126-0

1-107-36166-4

1-107-37031-0

1-299-40433-2

1-107-36411-6

0-511-89252-7

0-511-60069-0