Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.
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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
Über das Produkt
This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space.
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This chapter contains a preliminary discussion of the aims and philosophy of the book, and is not logically part of the course. Lesen Sie die erste Seite
Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
This chapter contains a preliminary discussion of the aims and philosophy of the book, and is not logically part of the course. Lesen Sie die erste Seite
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Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
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24 von 25 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen
"Undergraduate" in the best way
24. September 2000
Von Colin McLarty
- Veröffentlicht auf Amazon.com
Format:Taschenbuch
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 von 4 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen
Not my favorite math book
6. Juni 2011
Von N. Tung
- Veröffentlicht auf Amazon.com
Format:Taschenbuch|Von Amazon bestätigter Kauf
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 [...]
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 [...]
3.0 von 5 Sternen
almost
28. Oktober 2012
Von aps
- Veröffentlicht auf Amazon.com
Format:Taschenbuch
This book has a particularly endearing feature - the author's personality. It is quite useful in indicating what topics are important. However it is lacking in explanations (for self-study). Consequently I look at the presentation here and then go to "Dummit & Foote" to get an understanding. Also the notation is not fully defined so it adds another layer.
By the way, "Atiyah and Macdonald" is at least just as bad.
Perhaps these are more viable when used in a course with an instructor. Then they can serve as a nice outline.
By the way, "Atiyah and Macdonald" is at least just as bad.
Perhaps these are more viable when used in a course with an instructor. Then they can serve as a nice outline.
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