Continuous and Discrete Modules / Saad H. Mohamed, Bruno J. Müller.

By: Mohamed, Saad H [author.]Contributor(s): Müller, Bruno J [author.]Material type: TextTextSeries: London Mathematical Society Lecture Note Series ; no. 147Publisher: Cambridge : Cambridge University Press, 1990Description: 1 online resource (140 pages) : digital, PDF file(s)Content type: text Media type: computer Carrier type: online resourceISBN: 9780511600692 (ebook)Other title: Continuous & Discrete ModulesSubject(s): Injective modules (Algebra) | Projective modules (Algebra) | Representations of rings (Algebra) | Decomposition (Mathematics)Additional physical formats: Print version: : No titleDDC classification: 512/.4 LOC classification: QA247 | .M615 1990Online resources: Click here to access online 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.
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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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