I'm looking for a good book in commutative algebra, so I ask here for some advice. My ideal book should be:
-More comprehensive than Atiyah-MacDonald
-More readable than Matsumura (maybe better organized?)
-Less thick than Eisenbud, and more to the point
To put this in context, I'm an algebraic geometer, so I know enough commutative algebra, but I didn't study it systematically (apart from a first course on A-M which I followed as an undergraduate); rather I learned the things I needed from time to time. So I would like to give me an occasion to get a better grasp on the subject.
EDIT: I will be more specific about the level. As I said I already had a course on Atiyah-MacDonald, and I know that material well, so I'm not interested in books of a comparable level. But I'm not completely familiar with Cohen-Macaulay rings and the relationship between regular sequences and the Koszul complex for example. And I know very little of Gorenstein rings and duality. So I'm looking for something a little bit more sophisticated than what has been already proposed. Yes, I know Eisenbud does these things but it's easy to get lost in that book. Something more to the point would be nice.
Best Answer
For a reference on Cohen-Macaulay and Gorenstein rings, you can try "Cohen-Macaulay rings" by Bruns-Herzog.
Also, Huneke's lecture note "Hyman Bass and Ubiquity: Gorenstein Rings" is a great introduction to Gorenstein rings, very easy to read and to the point, I highly recommend it.
EDIT: Since this question is already bumped up, I will take this opportunity to make a longer list.
There are of course some classic references which are still very useful (I find myself having to look in them quite often despite the new sources available): Bourbaki, EGA IV, Serre's "Local Algebras" (very nice read and culminated in the beautiful Serre intersection formula).
There has been some work done in commutative algebra since the 60s, so here is a more up-to-date list of reference for some currently active topics (Disclaimer: I am not an expert in any of these, the list was formed by randomly looking at my bookself, and put in alphabetical order (-:). This is community-wiki, so feel free to add or edit or suggest things you found missing.
Cohen-Macaulay modules, from a representation theory perspective: Yoshino is excellent. Another one is being written.
Combinatorial commutative algebra: Miller-Sturmfels.
Free resolutions (over non-regular rings): Avramov lecture note
Geometry of syzygies: Eisenbud, shorter but free version here.
Homological conjectures: Hochster, Roberts (more connections to intersection theory), Hochster notes.
Integral closures: Huneke-Swanson, which is available free at the link.
Intersection theory done in a purely algebraic way: Flenner-O'Carrol-Vogel (for a very interesting story about this, see Eisenbud beautiful reminiscences, especially page 4)
Local Cohomology: Brodmann-Sharp, Huneke's lecture note (very easy to read), 24 hours of local cohomology (I have been told that this one was a pain to write, which is probably a good sign).
Tight closure and characteristic $p$ method: Huneke, Karen Smith's lecture note (more geometric, number 24 here), and of course many well-written introductions available on Hochster website.