Customer Reviews

Undergraduate Commutative Algebra (London Mathematical Society Student Texts)

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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.

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 [...]