• Lectures on Modules and Rings
  • Lectures on Modules and Rings
Band 189

Lectures on Modules and Rings

Aus der Reihe

Lectures on Modules and Rings

Ebenfalls verfügbar als:

Gebundenes Buch

Gebundenes Buch

ab Fr. 95.90
Taschenbuch

Taschenbuch

ab Fr. 95.90
eBook

eBook

ab Fr. 114.90

Fr. 95.90

inkl. MwSt, Versandkostenfrei

Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

18.09.2012

Verlag

Springer Us

Seitenzahl

557

Maße (L/B/H)

23.5/15.5/3.2 cm

Beschreibung

Rezension

"As in the previous book, the presentation is extremely clear and incisive and the exercises are both interesting and challenging. Without a doubt, the book could indeed serve as a textbook for a very good---though definitely formidable---graduate course in ring theory. The author is the first to admit, in his introduction, that he is far from having covered all of the interesting topics in noncommutative ring theory. Therefore, given the high level of presentation of the two books he has already published, one can only hope that a third volume will be in the offing, despite his "solemn pledge" to the contrary."--MATHEMATICAL REVIEWS

Details

Einband

Taschenbuch

Erscheinungsdatum

18.09.2012

Verlag

Springer Us

Seitenzahl

557

Maße (L/B/H)

23.5/15.5/3.2 cm

Gewicht

879 g

Auflage

Softcover reprint of the original 1st ed. 1999

Sprache

Englisch

ISBN

978-1-4612-6802-4

Herstelleradresse

Springer US, New York, N.Y.
Heidelberger Platz 3
14197 Berlin
Deutschland
Email: sdc-bookservice@springer.com
Telephone: +49 6221 3454301
Fax: +49 6221 3454229

Weitere Bände von Graduate Texts in Mathematics

Unsere Kundinnen und Kunden meinen

0.0

0 Bewertungen

Informationen zu Bewertungen

Zur Abgabe einer Bewertung ist eine Anmeldung im Konto notwendig. Die Authentizität der Bewertungen wird von uns nicht überprüft. Wir behalten uns vor, Bewertungstexte, die unseren Richtlinien widersprechen, entsprechend zu kürzen oder zu löschen.

Verfassen Sie die erste Bewertung zu diesem Artikel

Helfen Sie anderen Kund*innen durch Ihre Meinung

Erste Bewertung verfassen

Unsere Kundinnen und Kunden meinen

0.0

0 Bewertungen filtern

  • Lectures on Modules and Rings
  • Lectures on Modules and Rings
  • 1 Free Modules, Projective, and Injective Modules.- 1. Free Modules.- 1A. Invariant Basis Number (IBN).- 1B. Stable Finiteness.- 1C. The Rank Condition.- 1D. The Strong Rank Condition.- 1E. Synopsis.- Exercises for &x00A7;1.- 2. Projective Modules.- 2A. Basic Definitions and Examples.- 2B. Dual Basis Lemma and Invertible Modules.- 2C. Invertible Fractional Ideals.- 2D. The Picard Group of a Commutative Ring.- 2E. Hereditary and Semihereditary Rings.- 2F. Chase Small Examples.- 2G. Hereditary Artinian Rings.- 2H. Trace Ideals.- Exercises for &x00A7;2.- 3. Injective Modules.- 3A. Baer’s Test for Injectivity.- 3B. Self-Injective Rings.- 3C. Injectivity versus Divisibility.- 3D. Essential Extensions and Injective Hulls.- 3E. Injectives over Right Noetherian Rings.- 3F. Indecomposable Injectives and Uniform Modules.- 3G. Injectives over Some Artinian Rings.- 3H. Simple Injectives.- 31. Matlis’ Theory.- 3J. Some Computations of Injective Hulls.- 3K. Applications to Chain Conditions.- Exercises for &x00A7;3.- 2 Flat Modules and Homological Dimensions.- 4. Flat and Faithfully Flat Modules.- 4A. Basic Properties and Flatness Tests.- 4B. Flatness, Torsion-Freeness, and von Neumann Regularity.- 4C. More Flatness Tests.- 4D. Finitely Presented (f.p.) Modules.- 4E. Finitely Generated Flat Modules.- 4F. Direct Products of Flat Modules.- 4G. Coherent Modules and Coherent Rings.- 4H. Semihereditary Rings Revisited.- 41. Faithfully Flat Modules.- 4J. Pure Exact Sequences.- Exercises for &x00A7;4.- 5. Homological Dimensions.- 5A. Schanuel’s Lemma and Projective Dimensions.- 5B. Change of Rings.- 5C. Injective Dimensions.- 5D. Weak Dimensions of Rings.- 5E. Global Dimensions of Semiprimary Rings.- 5F. Global Dimensions of Local Rings.- 5G. Global Dimensions of Commutative Noetherian Rings.- Exercises for &x00A7;5.- 3 More Theory of Modules.- 6. Uniform Dimensions, Complements, and CS Modules.- 6A. Basic Definitions and Properties.- 6B. Complements and Closed Submodules.- 6C. Exact Sequences and Essential Closures.- 6D. CS Modules: Two Applications.- 6E. Finiteness Conditions on Rings.- 6F. Change of Rings.- 6G. Quasi-Injective Modules.- Exercises for &x00A7;6.- 7. Singular Submodules and Nonsingular Rings.- 7A. Basic Definitions and Examples.- 7B. Nilpotency of the Right Singular Ideal.- 7C. Goldie Closures and the Reduced Rank.- 7D. Baer Rings and Rickart Rings.- 7E. Applications to Hereditary and Semihereditary Rings.- Exercises for &x00A7;7.- 8. Dense Submodules and Rational Hulls.- 8A. Basic Definitions and Examples.- 8B. Rational Hull of a Module.- 8C. Right Kasch Rings.- Exercises for &x00A7;8.- 4 Rings of Quotients.- 9. Noncommutative Localization.- 9A. “The Good’.- 9B. “The Bad’.- 9C. “The Ugly”.- 9D. An Embedding Theorem of A. Robinson.- Exercises for &x00A7;9.- 10. Classical Rings of Quotients.- 10A. Ore Localizations.- 10B. Right Ore Rings and Domains.- 10C. Polynomial Rings and Power Series Rings.- 10D. Extensions and Contractions.- Exercises for
    10.- 11. Right Goldie Rings and Goldie’s Theorems.- 11A. Examples of Right Orders.- 11B. Right Orders in Semisimple Rings.- 11C. Some Applications of Goldie’s Theorems.- 11D. Semiprime Rings.- 11E. Nil Multiplicatively Closed Sets.- Exercises for &x00A7;11.- 12. Artinian Rings of Quotients.- 12A. Goldie’s ?-Rank.- 12B. Right Orders in Right Artinian Rings.- 12C. The Commutative Case.- 12D. Noetherian Rings Need Not Be Ore.- Exercises for &x00A7;12.- 5 More Rings of Quotients.- 13. Maximal Rings of Quotients.- 13A. Endomorphism Ring of a Quasi-Injective Module.- 13B. Construction of Qrmax(R).- 13C. Another Description of Qrmax(R).- 13D. Theorems of Johnson and Gabriel.- Exercises for
    13.- 14. Martindale Rings of Quotients.- 14A. Semiprime Rings Revisited.- 14B. The Rings Qr(R) and Qs(R).- 14C. The Extended Centroid.- 14D. Characterizations of and Qr(R) and Qs(R).- 14E. X-Inner Automorphisms.- 14F. A Matrix Ring Example.- Exercises for &x00A7;14.- 6 Frobenius and Quasi-Frobenius Rings.- 15. Quasi-Frobenius Rings.- 15A. Basic Definitions of QF Rings.- 15B. Projectives and Injectives.- 15C. Duality Properties.- 15D. Commutative QF Rings, and Examples.- Exercises for
    15.- 16. Frobenius Rings and Symmetric Algebras.- 16A. The Nakayama Permutation.- 16B. Definition of a Frobenius Ring.- 16C. Frobenius Algebras and QF Algebras.- 16D. Dimension Characterizations of Frobenius Algebras.- 16E. The Nakayama Automorphism.- 16F. Symmetric Algebras.- 16G. Why Frobenius?.- Exercises for &x00A7;16.- 7 Matrix Rings, Categories of Modules, and Morita Theory.- 17. Matrix Rings.- 17A. Characterizations and Examples.- 17B. First Instance of Module Category Equivalences.- 17C. Uniqueness of the Coefficient Ring.- Exercises for &x00A7;17.- 18. Morita Theory of Category Equivalences.- 18A. Categorical Properties.- 18B. Generators and Progenerators.- 18C. The Morita Context.- 18D. Morita I, II, III.- 18E. Consequences of the Morita Theorems.- 18F. The Category ? [M].- Exercises for &x00A7;18.- 19. Morita Duality Theory.- 19A. Finite Cogeneration and Cogenerators.- 19B. Cogenerator Rings.- 19C. Classical Examples of Dualities.- 19D. Morita Dualities: Morita I.- 19E. Consequences of Morita I.- 19F. Linear Compactness and Reflexivity.- 19G. Morita Dualities: Morita II.- Exercises for &x00A7;19.- References.- Name Index.