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.
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Editorial Reviews
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"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
MAA Reviews, Darren Glass
Book Description
This 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. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.
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First Sentence:
After a review of the definition and basic properties of noetherian modules and rings, we introduce a few classes of examples of notherian rings, which will serve to illustrate and support the later theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
right denominator set, second layer condition, right nonsingular ring, affiliated series, noetherian bimodules, affiliated primes, uniform right ideal, torsionfree right, critical composition series, essential right ideal, prime factor rings, prime noetherian ring, right noetherian ring, bounded noetherian rings, classical quotient ring, simple noetherian rings, differential operator ring, annihilator primes, noetherian ring theory, right artinian ring, finite ring extensions, right primitive ideal, simple artinian ring, triangular matrix ring, patch topology Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Jacobson's Conjecture, Small's Theorem, Krull Intersection Theorem, Lenagan's Theorem, Nakayama's Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
After a review of the definition and basic properties of noetherian modules and rings, we introduce a few classes of examples of notherian rings, which will serve to illustrate and support the later theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
right denominator set, second layer condition, right nonsingular ring, affiliated series, noetherian bimodules, affiliated primes, uniform right ideal, torsionfree right, critical composition series, essential right ideal, prime factor rings, prime noetherian ring, right noetherian ring, bounded noetherian rings, classical quotient ring, simple noetherian rings, differential operator ring, annihilator primes, noetherian ring theory, right artinian ring, finite ring extensions, right primitive ideal, simple artinian ring, triangular matrix ring, patch topology Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Jacobson's Conjecture, Small's Theorem, Krull Intersection Theorem, Lenagan's Theorem, Nakayama's Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 13
books:
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13
books
cite this book:
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- Krull Dimension (Memoirs of the American Mathematical Society) by Robert Gordon on page 239, and page 240
- Ring Theory (Lecture notes in pure and applied mathematics ; 40) by Oystaeyen in Back Matter (1), and Back Matter (2)
- Polynomial identities in ring theory, Volume 84 (Pure and Applied Mathematics) by Author Unknown in Back Matter
- Introduction To Commutative Algebra by Michael Atiyah in Back Matter
- Localization in Noetherian Rings (London Mathematical Society Lecture Note Series) by A. V. Jategaonkar in Back Matter
See all 13 books this book cites
- Hopf Algebras and Quantum Groups (Lecture Notes in Pure and Applied Mathematics) by Stefaan Caenepeel on page 187
- Lectures on Modules and Rings (Graduate Texts in Mathematics 189) by T. Y. Lam in Back Matter
- Abelian Groups, Rings, Modules, and Homological Algebra (Lecture Notes in Pure and Applied Mathematics) by Pat Goeters on page 118
- Algebra (Springer-Lehrbuch) (German Edition) by Jens Carsten Jantzen in Back Matter
- Modules and Rings by John Dauns in Back Matter
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