I certainly agree with Long's suggestion on Bruns and Herzog above. From a more geometric perspective You can also move from there to "Residues and Duality" if you'd like and there are other sources for that as well, Brian Conrad's book, Lipman's notes, etc. Coming from a more geometric perspective originally myself, I didn't really get Bruns and Herzog chapter 3 until I did this. For Eisenbud's book, perhaps you should take it chapter by chapter. Many chapters don't really rely on anything and can be read out of context.
This makes it a very valuable reference. I learned commutative algebra in the same way you describe: Atiyah-MacDonald and then picking things up along the way. I don't know if your ideal book exists or not, but I can give you one nice reference: Mel Hochster's lecture notes for Math and , available from his webpage.
To give the opposite suggestion from Bart, I was going to recommend Matsumura's Commutative ring theory as opposed to his Commutative algebra. I have said why at length on the "unanswered questions" thread asking exactly Pete's question. Briefly, Ring theory is clearer, better organized, argued more fully, with more exercises and answers , references, with a better index, and easier to read.
Probably because Miles Reid rendered it into English, and possibly also because Matsumura got to revise his first book, which was almost a set of excellent, and advanced class lecture notes. At least two of us who took Matsumura's class in Sevin Recillas and I seem to like the second book. Sevin owned and recommended it when i complained I had difficulty using the original book. Since I am judging based on what appears on Amazon, I cannot be positive it contains every result I want to reference, but from the table of contents I would guess it does.
I also like Zariski and Samuel for clarity, but homological methods were introduced just as that book was finished. Sign up to join this community. The best answers are voted up and rise to the top. Reference book for commutative algebra Ask Question. Asked 11 years, 10 months ago. Active 7 months ago. Viewed 16k times. My ideal book should be: -More comprehensive than Atiyah-MacDonald -More readable than Matsumura maybe better organized?
Improve this question. Moreover, I don't find it boring, but that's not my main point. David Eisenbud is an actual living person -- with internet access.
He is a very nice man, one of the world's leading commutative algebraists, and one of the most influential and well connected mathematicians I know. It has nothing to do with the author being a nice person or not. If a nice mathematician writes a wrong paper, would it be inappropriate to say his work is wrong?
It is a well-known principle of reviewing that one does not make negative comments without justification, let alone unjustifiable ones. Clark Pete-may I call you Pete? A text's job above all is to educate and it's essential the experience be a positive one for that to occur. Fortunately,that hasn't happened often-most of the books I've reviewed have been quite good,some excellent.
Show 11 more comments. Active Oldest Votes. Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry.
The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text.
One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it.
Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained.
Novel results and presentations are scattered throughout the text. The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible. Skip to main content Skip to table of contents. Create a free Team What is Teams? Learn more.
Commutative Algebra books [duplicate] Ask Question. Asked 4 years, 8 months ago. Active 4 years, 8 months ago. Viewed times. Martin Sleziak What do you want to study after this? He starts from a very easy level and builds up on that. Then you can move to a less detailed book like Matsumura's Commutative Ring Theory or Eisenbud's book.
I am not sure what I want to study after this, I am just trying to acquire a good math background in general. Add a comment.
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