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 ?