So I was searching about books for commutative algebra. I have read most of the algebra namely galois theory and field theory and basic algebra from Dummit Foote. So I was thinking about studying commutative algebra from Dummit Foote. Although most of the suggestion I have seen for the book for commutative algebra is Atiyah Mcdonald. So it will be great if anyone can tell me how well commutative algebra is written in Dummit Foote.

  • $\begingroup$ D&F is a good book for beginners, but it's too verbose to be a reference book. They do treat valuation rings, integral extensions, localisation, and Zariski topology, which I think are very good subjects for a first course in commutative algebra. But IIRC they don't talk about Krull dimension. Atiyah--McDonald is great. My personal favorite is Eisenbud's "Commutative Algebra with a view towards algebraic geometry". Everything is in there! $\endgroup$ – Ehsaan May 26 at 15:04
  • $\begingroup$ But the thing is I don't have much exposure to topology. And I have heard eisenbud has application of topology very much. That's why I was reluctant $\endgroup$ – user631697 May 26 at 18:09
  • $\begingroup$ Maybe you can learn them hand-in-hand. You've seen basic ring theory, so you should be somewhat ready. Topology and commutative rings are inextricable, as Eisenbud shows. $\endgroup$ – Ehsaan May 26 at 20:47

May be its a bit late to comment,but you can go through Basic Commutative Algebra by Dr. Balwant Singh. It is a great commutative algebra book and also covers some interesting topics in Homological Algebra. Dummit and Foote is a great book in its own right but certain things like resolutions, category theory, derived functors are well written in Balwant Singh book.

  • $\begingroup$ Balwant sing, are you somehow from cmi? $\endgroup$ – user631697 Sep 16 at 11:33
  • $\begingroup$ No no I am not from CMI, but you can give it a look.( the book) if you find it worthwhile let me know. $\endgroup$ – ZOne Sep 16 at 11:36
  • $\begingroup$ No actually a prof who was extremely close with the author exactly told me this book, and as you have said that book along with a book by Gopalakrishnan is really good for commutative algebra. That's why I thought. $\endgroup$ – user631697 Sep 16 at 11:38
  • $\begingroup$ Ah I see , actually I am doing PhD under Balwant sir's student. So my supervisor advised me to go through that book. $\endgroup$ – ZOne Sep 16 at 11:40
  • $\begingroup$ Ohh okay okay that's why, what's his name if you don't mind. $\endgroup$ – user631697 Sep 16 at 11:41

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