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A Course in Ring Theory
 
Donald S. Passman University of Wisconsin, Madison, WI
Front Cover for A Course in Ring Theory
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN: 978-0-8218-3680-4
Product Code: CHEL/348.H
List Price: $53.00
MAA Member Price: $47.70
AMS Member Price: $47.70
Electronic ISBN: 978-1-4704-2999-7
Product Code: CHEL/348.H.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $45.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $79.50
MAA Member Price: $71.55
AMS Member Price: $71.55
Front Cover for A Course in Ring Theory
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A Course in Ring Theory
Donald S. Passman University of Wisconsin, Madison, WI
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN:  978-0-8218-3680-4
Product Code:  CHEL/348.H
List Price: $53.00
MAA Member Price: $47.70
AMS Member Price: $47.70
Electronic ISBN:  978-1-4704-2999-7
Product Code:  CHEL/348.H.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $45.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $79.50
MAA Member Price: $71.55
AMS Member Price: $71.55
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 3482004; 306 pp
    MSC: Primary 16; Secondary 19;

    First published in 1991, this book contains the core material for an undergraduate first course in ring theory. Using the underlying theme of projective and injective modules, the author touches upon various aspects of commutative and noncommutative ring theory. In particular, a number of major results are highlighted and proved.

    Part I, "Projective Modules", begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderburn, Artinian and Noetherian rings, hereditary rings, Dedekind domains, etc.). This part concludes with an introduction and discussion of the concepts of the projective dimension.

    Part II, "Polynomial Rings", studies these rings in a mildly noncommutative setting. Some of the results proved include the Hilbert Syzygy Theorem (in the commutative case) and the Hilbert Nullstellensatz (for almost commutative rings).

    Part III, "Injective Modules", includes, in particular, various notions of the ring of quotients, the Goldie Theorems, and the characterization of the injective modules over Noetherian rings.

    The book contains numerous exercises and a list of suggested additional reading. It is suitable for graduate students and researchers interested in ring theory.

    Readership

    Graduate students and research mathematicians interested in ring theory.

  • Table of Contents
     
     
    • Projective modules
    • Modules and homomorphisms
    • Projective modules
    • Completely reducible modules
    • Wedderburn rings
    • Artinian rings
    • Hereditary rings
    • Dedekind domains
    • Projective dimension
    • Tensor products
    • Local rings
    • Polynomial rings
    • Skew polynomial rings
    • Grothendieck groups
    • Graded rings and modules
    • Induced modules
    • Syzygy theorem
    • Patching theorem
    • Serre conjecture
    • Big projectives
    • Generic flatness
    • Nullstellensatz
    • Injective modules
    • Injective modules
    • Injective dimension
    • Essential extensions
    • Maximal ring of quotients
    • Classical ring of quotients
    • Goldie rings
    • Uniform dimension
    • Uniform injective modules
    • Reduced rank
  • Reviews
     
     
    • "There seems to be an emerging consensus as to what material should constitute the core of a first course in module-theoretic ring theory ... The book ... is definitely within the bounds of that consensus ... presentation is clear, the proofs are often quite ingenious and the exercises are well chosen ... definitely suitable for use as a textbook."

      Mathematical Reviews
    • This excellently written book, which has been published originally by Wadsworthand Brooks in 1991, is already a classic ... A book recommendable now as before!

      Monatshefte für Mathematik
  • Request Review Copy
  • Get Permissions
Volume: 3482004; 306 pp
MSC: Primary 16; Secondary 19;

First published in 1991, this book contains the core material for an undergraduate first course in ring theory. Using the underlying theme of projective and injective modules, the author touches upon various aspects of commutative and noncommutative ring theory. In particular, a number of major results are highlighted and proved.

Part I, "Projective Modules", begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderburn, Artinian and Noetherian rings, hereditary rings, Dedekind domains, etc.). This part concludes with an introduction and discussion of the concepts of the projective dimension.

Part II, "Polynomial Rings", studies these rings in a mildly noncommutative setting. Some of the results proved include the Hilbert Syzygy Theorem (in the commutative case) and the Hilbert Nullstellensatz (for almost commutative rings).

Part III, "Injective Modules", includes, in particular, various notions of the ring of quotients, the Goldie Theorems, and the characterization of the injective modules over Noetherian rings.

The book contains numerous exercises and a list of suggested additional reading. It is suitable for graduate students and researchers interested in ring theory.

Readership

Graduate students and research mathematicians interested in ring theory.

  • Projective modules
  • Modules and homomorphisms
  • Projective modules
  • Completely reducible modules
  • Wedderburn rings
  • Artinian rings
  • Hereditary rings
  • Dedekind domains
  • Projective dimension
  • Tensor products
  • Local rings
  • Polynomial rings
  • Skew polynomial rings
  • Grothendieck groups
  • Graded rings and modules
  • Induced modules
  • Syzygy theorem
  • Patching theorem
  • Serre conjecture
  • Big projectives
  • Generic flatness
  • Nullstellensatz
  • Injective modules
  • Injective modules
  • Injective dimension
  • Essential extensions
  • Maximal ring of quotients
  • Classical ring of quotients
  • Goldie rings
  • Uniform dimension
  • Uniform injective modules
  • Reduced rank
  • "There seems to be an emerging consensus as to what material should constitute the core of a first course in module-theoretic ring theory ... The book ... is definitely within the bounds of that consensus ... presentation is clear, the proofs are often quite ingenious and the exercises are well chosen ... definitely suitable for use as a textbook."

    Mathematical Reviews
  • This excellently written book, which has been published originally by Wadsworthand Brooks in 1991, is already a classic ... A book recommendable now as before!

    Monatshefte für Mathematik
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