FPF Ring Theory: Faithful Modules and Generators of Mod-R: 88 (London Mathematical Society Lecture Note Series, Series Number 88) - Softcover
Book 75 of 387: London Mathematical Society Lecture Notes
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.
"synopsis" may belong to another edition of this title.
Book Description
This work, the result of a decade of work by the authors, includes all known theorems on the subject of noncommutative FPF rings. It is the first book on FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules.
"About this title" may belong to another edition of this title.
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FPF Ring Theory: Faithful Modules and Generators of Mod-R (London Mathematical Society Lecture Note Series 88)
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ISBN 13: 9780521277389
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FPF Ring Theory : Faithful Modules and Generators of Mod-R
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ISBN 10: 0521277388
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FPF Ring Theory: Faithful Modules and Generators of Mod-R: 88 (London Mathematical Society Lecture Note Series, Series Number 88)
Published by
Cambridge University Press, 1984
ISBN 10: 0521277388
ISBN 13: 9780521277389
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FPF Ring Theory: Faithful Modules and Generators of Mod-R (London Mathematical Society Lecture Note Series, Series Number 88)
Published by
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ISBN 10: 0521277388
ISBN 13: 9780521277389
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Fpf Ring Theory : Faithful Modules and Generators of Mod-R
Published by
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ISBN 10: 0521277388
ISBN 13: 9780521277389
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Fpf Ring Theory : Faithful Modules and Generators of Mod-R
Published by
Cambridge University Press, 1984
ISBN 10: 0521277388
ISBN 13: 9780521277389
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Fpf Ring Theory: Faithful Modules and Generators of Mod-R (Paperback)
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Cambridge University Press, Cambridge, 1984
ISBN 10: 0521277388
ISBN 13: 9780521277389
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Paperback. Condition: new. Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521277389
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Fpf Ring Theory: Faithful Modules and Generators of Mod-R (Paperback or Softback)
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FPF Ring Theory: Faithful Modules and Generators of Mod-R
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Paperback. Condition: Brand New. 176 pages. 8.90x6.08x0.48 inches. In Stock. This item is printed on demand. Seller Inventory # __0521277388
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Fpf Ring Theory : Faithful Modules and Generators of Mod-R
Published by
Cambridge University Press, 1984
ISBN 10: 0521277388
ISBN 13: 9780521277389
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