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Cover: 9780387988504 | Exercises in Modules and Rings | T. Y. Lam | Buch | xviii | Englisch
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Exercises in Modules and Rings
Buch von T. Y. Lam
Sprache: Englisch

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Beschreibung
The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching obligations and intermittent intervention of other projects caused prolonged delays in the work on this volume. Only a lucky break in my schedule in 2006 enabled me to put the finishing touches on the completion of this long overdue book. This book is intended to serve a dual purpose. First, it is designed as a "problem book" for Lectures. As such, it contains the statements and full solutions of the many exercises that appeared in Lectures. Second, this book is also offered as a reference and repository for general information in the theory of modules and rings that may be hard to find in the standard textbooks in the field. As a companion volume to Lectures, this work covers the same math­ ematical material as its parent work; namely, the part of ring theory that makes substantial use of the notion of modules. The two books thus share the same table of contents, with the first half treating projective, injective, and flat modules, homological and uniform dimensions, and the second half dealing with noncommutative localizations and Goldie's theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, conclud­ ing with Morita's theory of category equivalences and dualities.
The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching obligations and intermittent intervention of other projects caused prolonged delays in the work on this volume. Only a lucky break in my schedule in 2006 enabled me to put the finishing touches on the completion of this long overdue book. This book is intended to serve a dual purpose. First, it is designed as a "problem book" for Lectures. As such, it contains the statements and full solutions of the many exercises that appeared in Lectures. Second, this book is also offered as a reference and repository for general information in the theory of modules and rings that may be hard to find in the standard textbooks in the field. As a companion volume to Lectures, this work covers the same math­ ematical material as its parent work; namely, the part of ring theory that makes substantial use of the notion of modules. The two books thus share the same table of contents, with the first half treating projective, injective, and flat modules, homological and uniform dimensions, and the second half dealing with noncommutative localizations and Goldie's theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, conclud­ ing with Morita's theory of category equivalences and dualities.
Zusammenfassung

This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.

Inhaltsverzeichnis
Free Modules, Projective, and Injective Modules.- Flat Modules and Homological Dimensions.- More Theory of Modules.- Rings of Quotients.- More Rings of Quotients.- Frobenius and Quasi-Frobenius Rings.- Matrix Rings, Categories of Modules and Morita Theory.
Details
Erscheinungsjahr: 2006
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Problem Books in Mathematics
Inhalt: xviii
414 S.
ISBN-13: 9780387988504
ISBN-10: 0387988505
Sprache: Englisch
Herstellernummer: 10724957
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lam, T. Y.
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Problem Books in Mathematics
Maße: 241 x 160 x 29 mm
Von/Mit: T. Y. Lam
Erscheinungsdatum: 15.12.2006
Gewicht: 0,816 kg
Artikel-ID: 102266121
Zusammenfassung

This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.

Inhaltsverzeichnis
Free Modules, Projective, and Injective Modules.- Flat Modules and Homological Dimensions.- More Theory of Modules.- Rings of Quotients.- More Rings of Quotients.- Frobenius and Quasi-Frobenius Rings.- Matrix Rings, Categories of Modules and Morita Theory.
Details
Erscheinungsjahr: 2006
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Problem Books in Mathematics
Inhalt: xviii
414 S.
ISBN-13: 9780387988504
ISBN-10: 0387988505
Sprache: Englisch
Herstellernummer: 10724957
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lam, T. Y.
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Problem Books in Mathematics
Maße: 241 x 160 x 29 mm
Von/Mit: T. Y. Lam
Erscheinungsdatum: 15.12.2006
Gewicht: 0,816 kg
Artikel-ID: 102266121
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