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An Introduction to Noncommutative Noetherian Rings

2nd Edition

$69.99 (P)

Part of London Mathematical Society Student Texts

  • Date Published: July 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521545372

$ 69.99 (P)
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About the Authors
  • This introduction to noncommutative noetherian rings, accessible to anyone with a basic background in abstract algebra, can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory material is given, and exercises are integrated throughout. New material includes the basic types of quantum groups.

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

    "Readers of the first edition will notice a number of changes in this edition, including a restrucuring of the topics, many more explicit examples, and an increased emphasis on quantum groups, a subject which has flourished in the decade that has passed since the first edition...This level of explicitness would make large parts of the book accessible even to an undergraduate who has only completed a first course in algebra, although the target audience is primarily at the graduate student level."
    MAA Reviews, Darren Glass

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    Product details

    • Edition: 2nd Edition
    • Date Published: July 2004
    • 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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