A good commutative algebra book [duplicate]
Possible Duplicate:
Reference request: introduction to commutative algebra
I'm looking for a good book on commutative algebra covering most of (but not limited to) :
- Basic Galois theory and Module algebra
- Primary decomposition of ideals
- Zariski topology
- Nullstellensatz, Hauptidealsatz
- Noether's normalization
- Ring extensions
- "Going up" and "Going down"
The emphasis is on the approach, as I would like a book giving a good geometric intuition of ring theory that I could use as a solid basis to start learning algebraic geometry.
All in all, do you remember a book that gave you a deeper geometric insight of commutative algebra ?
Solution 1:
My top 3 :
Commutative Algebra: with a View Toward Algebraic Geometry, by D. Eisenbud, definitely. As Dylan said in the comments, “some will call it overly chatty but the geometry discussed there is worth everything”. To learn, nothing is too chatty, but to serve as a handbook, yes, this book might be a bit too chatty.
Commutative Algebra, by Bourbaki, exhaustive, once you will be confortable, not to learn.
Commutative Algebra I & II, by Zariski and Samuel, slightly old fashioned, but very pedagogic, and feature very interesting points of view, aimed at geometry.