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An Introduction to Noncommutative Noetherian Rings

2nd Edition

Part of London Mathematical Society Student Texts

  • Date Published: February 2005
  • availability: Available
  • format: Paperback
  • isbn: 9780521545372

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  • This 2004 introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. Material includes the basic types of quantum groups, which then serve as test cases for the theory developed.

    • Sketches of typical classes of application for motivation
    • Extensive explanatory discussion
    • Exercises integrated throughout the text
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    Reviews & endorsements

    '… well written and perfectly suits for both students beginning to study Ring theory and established mathematicians that are just interested in learning basics of the theory of Noetherian rings.' Zentralblatt MATH

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    Product details

    • Edition: 2nd Edition
    • Date Published: February 2005
    • format: Paperback
    • isbn: 9780521545372
    • length: 370 pages
    • dimensions: 225 x 157 x 23 mm
    • weight: 0.54kg
    • contains: 375 exercises
    • availability: Available
  • Table of Contents

    1. A few Noetherian rings
    2. Skew polynomial rings
    3. Prime ideals
    4. Semisimple modules, Artinian modules, and torsionfree modules
    5. Injective hulls
    6. Semisimple rings of fractions
    7. Modules over semiprime Goldie rings
    8. Bimodules and affiliated prime ideals
    9. Fully bounded rings
    10. Rings and modules of fractions
    11. Artinian quotient rings
    12. Links between prime ideals
    13. The Artin-Rees property
    14. Rings satisfying the second layer condition
    15. Krull dimension
    16. Numbers of generators of modules
    17. Transcendental division algebras.

  • Authors

    K. R. Goodearl, University of California, Santa Barbara
    K. R. Goodearl received his Ph.D. in 1971 from the University of Washington. Following an instructorship at the University of Chicago, he spent 19 years at the University of Utah. Since 1991, he has been a professor of mathematics at the University of California at Santa Barbara.

    R. B. Warfield, Jr
    R. B. Warfield Jr. received his Ph.D. in 1967 from Harvard University. Following a postdoctoral year at New Mexico State University, he joined the mathematics department of the University of Washington, where he was a professor until his death in 1989.

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