|
||||||||||||||||||||
|
||||||||||||||||||||
|
||||||||||||||||||||
よく一緒に購入されている商品
商品の説明
内容説明
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Book Description
This book is an attempt to write on commutative algebra in a way that includes the geometric ideas that played a great role in its formation; with a view, in short, towards Algebraic Geometry. The author provides a book that covers the material that graduate students studying Algebraic Geometry - and in particular those studying the book Algebraic Geometry by Robin Hartshorne - should know. The reader should have had one year of basic graduate algebra.
登録情報
|
この本のなか見！検索より
（詳細はこちら）
この商品を見た後に買っているのは？
カスタマーレビュー
最も参考になったカスタマーレビュー
10 人中、8人の方が、｢このレビューが参考になった｣と投票しています。
形式:ペーパーバック
僕が大学院時代、指導教官に薦められた本の中の一冊で、セミナーではこの本を使って勉強しました。ほとんどすべての本のに参考文献として載っている本でもあります。丁寧にかかれているので、学部生でも読みやすく、例も多く理解しやすいと思います。
Amazon.com で最も参考になったカスタマーレビュー (beta)
Amazon.com:
9件のカスタマーレビュー
39 人中、38人の方が、｢このレビューが参考になった｣と投票しています。
The standard text
2000/7/28
形式:ペーパーバック
This is often referred to as the standard text on commutative algebra.
It is an exceptionally good book on a subject that is normally difficult to get a handle on. Eisenbud's readable book gives intuitive and motivated proofs of even very technical results in commutative algebra, often illustrated with instructive examples, such as the useful figures illustrating embedded primes. A very nice feature is that he gives proofs to all the results in commutative algebra used by Robin Hartshorne's popular "Algebraic Geometry," making them a nice pair of books to read together.
I found this to be useful as a reference as well as a text. Most sections are fairly self-contained and many important topics are included in depth. I almost always find that it is the best place to learn any of the material covered.
This book belongs on the shelf of anyone learning algebraic geometry, although it will spend plenty of time off the shelf as well.
44 人中、37人の方が、｢このレビューが参考になった｣と投票しています。
Superb
2001/9/4
形式:ペーパーバック
If one is interested in taking on a thorough study of algebraic geometry, this book is a perfect starting point. The writing is excellent, and the student will find many exercises that illustrate and extend the results in each chapter. Readers are expected to have an undergraduate background in algebra, and maybe some analysis and elementary notions from differential geometry. Space does not permit a thorough review here, so just a brief summary of the places where the author has done an exceptional job of explaining or motivating a particular concept:
(1) The history of commutative algebra and its connection with algebraic geometry, for example the origin of the concept of an "ideal" of a ring as generalizing unique factorization.
(2) The discussion of the concept of localization, especially its origins in geometry. A zero dimensional ring (collection of "points") is a ring whose primes are all maximal, as expected.
(3) The theory of prime decomposition as a generalization of unique prime factorization. Primary decomposition is given a nice geometric interpretation in the book.
(4) Five different proofs of the Nullstellensatz discussed, giving the reader good insight on this important result.
(5) The geometric interpretation of an associated graded ring corresponding to the exceptional set in the blowup algebra.
(6) The notion of flatness of a module as a continuity of fibers and a test for this using the Tor functor.
(7) The characterization of Hensel's lemma as a version of Newton's method for solving equations. The geometric interpretation of the completion as representing the properties of a variety in neighborhoods smaller than Zariski open neighborhoods.
(8) The characterization of dimension using the Hilbert polynomial.
(9) The fiber dimension and the proof of its upper semicontinuity.
(10) The discussion of Grobner bases and flat families. Nice examples are given of a flat family connecting a finite set of ideals to their initial ideals.
(11) Computer algebra projects for the reader using the software packages CoCoA and Macaulay.
(12) The theory of differentials in algebraic geometry as a generalization of what is done in differential geometry.
(13) The discussion of how to construct complexes using tensor products and mapping cones in order to study the Koszul complex.
(14) The connection of the Koszul complex to the cotangent bundle of projective space.
(15) The geometric interpretation of the Cohen-Macauley property as a map to a regular variety.
13 人中、11人の方が、｢このレビューが参考になった｣と投票しています。
Excellent Book...very atypical for a math book, but I like it!
2007/12/17
形式:ペーパーバック
People tend to have strong feelings about this book. In my opinion, the people who dislike it are those who expect it to be like a typical graduate-level math book. This book is extremely atypical for a math book; it's not meant to be read linearly, and the topics in it do not follow a typical logical dependency. Personally, I find it to be outstanding; my only complaint about it is that I wish there were more books like it!
Commutative algebra and algebraic geometry are extremely difficult subjects requiring a great deal of background. This book is written as a sort of intermediary text between introductory abstract algebra books with a full and exposition of algebraic structures, and advanced, highly technical texts that can be difficult to follow and grasp on a technical level. As such, this book focuses on developing intuition, and discussing the history and motivation behind the various mathematical structures presented. It assumes that most of the other aspects of the subject, including both the elementary expositions, and the more advanced technical details, can be found elsewhere (although, believe me, this book certainly has its share of both elementary expositions and advanced technical details!)
I think this book is actually better for self-study than for use as a textbook. Most of the people I have known who have used it as a textbook have been frustrated with it. Either way, it needs to be supplemented by other books. Personally, on algebra, I like the Dummit and Foote, Isaacs, and Lang books. Those three books have very little overlap with each other, and very little overlap with this book, and they offer a very useful difference of perspectives where they do overlap! I also would recommend reading the more elementary book by Cox, Little, and O'Shea, which can help you get a feel for the subject of algebraic geometry. Many people see this book's primary purpose as preparation for Robin Hartshorne's "Algebraic Geometry". I can't say, however, how effective it is at that purpose, as no matter how far I get in this book, all but a few sections from that book still remain quite far beyond my grasp.
Commutative algebra and algebraic geometry are extremely difficult subjects requiring a great deal of background. This book is written as a sort of intermediary text between introductory abstract algebra books with a full and exposition of algebraic structures, and advanced, highly technical texts that can be difficult to follow and grasp on a technical level. As such, this book focuses on developing intuition, and discussing the history and motivation behind the various mathematical structures presented. It assumes that most of the other aspects of the subject, including both the elementary expositions, and the more advanced technical details, can be found elsewhere (although, believe me, this book certainly has its share of both elementary expositions and advanced technical details!)
I think this book is actually better for self-study than for use as a textbook. Most of the people I have known who have used it as a textbook have been frustrated with it. Either way, it needs to be supplemented by other books. Personally, on algebra, I like the Dummit and Foote, Isaacs, and Lang books. Those three books have very little overlap with each other, and very little overlap with this book, and they offer a very useful difference of perspectives where they do overlap! I also would recommend reading the more elementary book by Cox, Little, and O'Shea, which can help you get a feel for the subject of algebraic geometry. Many people see this book's primary purpose as preparation for Robin Hartshorne's "Algebraic Geometry". I can't say, however, how effective it is at that purpose, as no matter how far I get in this book, all but a few sections from that book still remain quite far beyond my grasp.
これらのレビューは参考になりましたか？
ご意見はクチコミでお聞かせください。
リストマニア
|
|
関連商品を探す
- 洋書 > Professional & Technical > Professional Science > Mathematics > Geometry & Topology
- 洋書 > Professional & Technical > Professional Science > Mathematics > Pure Mathematics
- 洋書 > Science > Mathematics > Geometry & Topology > Algebraic Geometry
- 洋書 > Science > Mathematics > Pure Mathematics > Algebra
- 洋書 > Science > Mathematics > Pure Mathematics > Group Theory
- 洋書 > Special Features > all foreign books
同じキーワードの商品を探す
フィードバック
- カタログ情報、または画像について報告
- 著者からのコメント
- 出版社からのコメント
|
