FPF Ring Theory: Faithful Modules and Generators of Mod-R (London Mathematical Society Lecture Note Series)

Faith, Carl; Page, Stanley

ISBN 10: 0521277388 / ISBN 13: 9780521277389

Published by Cambridge University Press, 1984

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Bibliographic Details

• Title: FPF Ring Theory: Faithful Modules and Generators of Mod-R (London Mathematical Society Lecture Note Series)
• Publisher: Cambridge University Press
• Publication Date: 1984
• Language: English
• ISBN 10: 0521277388
• ISBN 13: 9780521277389
• Binding: Paperback
• Condition: Very Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

About this title

Synopsis

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.

Book Description

The first book on FPF rings and the systematic use of the notion of a generator of the category mod-R of all R-modules and its relationship to faithful modules.