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FPF Ring Theory

FPF Ring Theory
Faithful Modules and Generators of Mod-R

Part of London Mathematical Society Lecture Note Series

  • Date Published: April 1984
  • availability: Available
  • format: Paperback
  • isbn: 9780521277389

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  • This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, K. Morita, T. Nakayama, R. Thrall, and more recently, W. Brandal, R. Pierce, T. Shores, R. and S. Wiegand and P. Vamos, among others. FPF rings include quasi-Frobenius rings (and thus finite rings over fields), pseudo-Frobenius (PF) rings (and thus injective cogenerator rings), bounded Dedekind prime rings and the following commutative rings; self-injective rings, Prufer rings, all rings over which every finitely generated module decomposes into a direct sum of cyclic modules (=FGC rings), and hence almost maximal valuation rings. Any product (finite or infinite) of commutative or self-basic PFP rings is FPF. A number of important classes of FPF rings are completely characterised including semiprime Neotherian, semiperfect Neotherian, perfect nonsingular prime, regular and self-injective rings. Finite group rings over PF or commutative injective rings are FPF. This work is the culmination of a decade of research and writing by the authors and includes all known theorems on the subject of noncommutative FPF rings. This book will be of interest to professional mathematicians, especially those with an interest in noncommutative ring theory and module theory.

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    Product details

    • Date Published: April 1984
    • format: Paperback
    • isbn: 9780521277389
    • length: 176 pages
    • dimensions: 230 x 153 x 13 mm
    • weight: 0.3kg
    • availability: Available
  • Table of Contents

    Preface
    Dedication and acknowledgement
    Introduction
    1. The basics
    2. Noncommutative semiperfect and semiprime (C) FPF rings
    3. Nonsingular FPF rings
    4. Goldie prime FPF rings with RRM and the structure of neotherian prime FPF rings
    5. Self-injective FPF rings, thin rings and FPF group rings
    Summary of the structure of FPF rings
    Open questions
    Bibliography
    Abbreviations and symbols
    Index.

  • Authors

    Carl Faith

    Stanley Page

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