FPF Ring Theory by Carl Faith
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FPF Ring Theory
By Carl Faith

FPF Ring Theory

Faithful Modules and Generators of Mod-R

By (author) See other recent books by Carl Faith See other recent books by Stanley Page
Series edited by N. J. Hitchin See other recent books by N. J. Hitchin
Format: Paperback

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FPF Ring Theory by Carl Faith

Book Description

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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Book Details

ISBN: 9780521277389
ISBN-10: 0521277388
Format: Paperback
(228mm x 152mm x 10mm)
Pages: 176
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 26-Apr-1984
Country of Publication: United Kingdom

Books By Author Carl Faith

Simple Noetherian Rings by Carl Faith Simple Noetherian Rings, Paperback (January 2009)

This work specifically surveys simple Noetherian rings.

» View all books by Carl Faith


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