In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins with a discussion of modules and Noetherian rings before moving on to finite extensions and the Noether normalization. Sections on the nullstellensatz and rings of fractions precede sections on primary decomposition and normal integral domains. This book is ideal for anyone seeking a primer on commutative algebra.
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'It gives a fresh picture of the subject for a new generation of students.' P. Scnezel, Zentralblatt fur Mathematik
'The author takes care to explain the geometric and number theoretic meaning of the algebraic methods and results presented. This makes the book perhaps more demanding, but surely much more interesting than the standard ones.' European Mathematical Society Newsletter
'Besides the usual topics ... there are some welcome geometrical illustrations, as well as some homespun philosophy.' Mathematica
'The author takes care to explain the geometric and number theoretic meaning of the algebraic methods and results presented. This makes the book perhaps more demanding, but surely much more interesting than the standard ones.' European Mathematical Society Newsletter
'Besides the usual topics ... there are some welcome geometrical illustrations, as well as some homespun philosophy.' Mathematica
Book Description
Showing the link between commutative ring theory and algebraic geometry, this book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. It is ideal for anyone seeking a primer on commutative algebra.
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24 of 25 people found the following review helpful:
5.0 out of 5 stars
"Undergraduate" in the best way,
By Colin McLarty (Chardon, OH USA) - See all my reviews
This review is from: Undergraduate Commutative Algebra (London Mathematical Society Student Texts) (Paperback)
The material in this book is not usually considered "undergraduate": Noether normalization, spectra of rings, discrete valuation rings, and more. But this book makes them very clear. It is more geometrical, and has more motivation, than Atiyah and MacDonald INTRODUCTION TO COMMUTATIVE ALGEBRA. It is briefer and more surveyable than Eisenbud COMMUTATIVE ALGEBRA. If you go on in the subject you will certainly need Eisenbud's book. This is a very good starter, and a good companion to Eisenbud if you are learning the material on your own.
3.0 out of 5 stars
Not my favorite math book,
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This review is from: Undergraduate Commutative Algebra (London Mathematical Society Student Texts) (Paperback)
I used this book for an undergraduate algebraic geometry class. Most of the class absolutely hated it; I didn't feel quite as strongly. The organization is not bad, and while most beginning problems are trivial, latter ones are interesting but not unreachable.
I like parsimonious texts, but at times the author goes too far, using unexplained notation (sorry I forget where.) More seriously, there's a lot of cases where the author trades providing intuition for parsimony; for example, writing that "prime implies irreducible, but the other way round is false in general". In my opinion, a simple example here would be worth the fraction of a page. Sorry I don't have a good reference to go to; I like the style of Lang's Algebra and Eisenbud's Commutative Algebra, but they may not be great introductory material. I've heard Dummit and Foote or Fraleigh are good; maybe check math.stackexchange for recommendations [...]
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Inside This Book
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First Sentence:
This chapter contains a preliminary discussion of the aims and philosophy of the book, and is not logically part of the course. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
integral dependence relation, determinant trick, multiplicative set, many prime ideals, nonzero prime ideal, primary decomposition, valuation ring, irreducible subvarieties, minimal nonzero, local ring, minimal prime ideals, maximal ideal, coordinate ring, integral domain, integral closure, ascending chain condition, minimal primes, ring homomorphism, nilpotent elements, polynomial ring Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proposition Let, Definition Let, Theorem Let, Emmy Noether, Proof Let, Ass All, Lemma Let, Noetherian A-module, Proof Suppose New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter contains a preliminary discussion of the aims and philosophy of the book, and is not logically part of the course. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
integral dependence relation, determinant trick, multiplicative set, many prime ideals, nonzero prime ideal, primary decomposition, valuation ring, irreducible subvarieties, minimal nonzero, local ring, minimal prime ideals, maximal ideal, coordinate ring, integral domain, integral closure, ascending chain condition, minimal primes, ring homomorphism, nilpotent elements, polynomial ring Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proposition Let, Definition Let, Theorem Let, Emmy Noether, Proof Let, Ass All, Lemma Let, Noetherian A-module, Proof Suppose 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 2
books:
5
books
cite this book:
- The Journey to the West, Vol. 1 by Wu Cheng-en on page 36
- Lectures on Lie Groups and Lie Algebras (London Mathematical Society Student Texts) by Roger W. Carter in Front Matter
- Potential Theory in the Complex Plane (London Mathematical Society Student Texts) by Dr Thomas Ransford in Front Matter
- A Primer of Algebraic D-Modules (London Mathematical Society Student Texts) by S. C. Coutinho in Front Matter
- An Introduction To Commutative Algebra: From The Viewpoint Of Normalization by Li HUISHI in Back Matter
- Elementary Algebraic Geometry (Student Mathematical Library, Vol. 20) (Student Mathematical Library, V. 20) by Klaus Hulek in Back Matter
- An Introduction to General Relativity (London Mathematical Society Student Texts) by L. P. Hughston in Front Matter
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