Noetherian and Artinian rings (reference)

Question

I started to study localization of rings and Noetherian and Artinian rings. Do you know any good references for these subjects? I'm using the one by Atiyah and Mcdonald. Is there another one? Thank you.

Answer 1

There are plenty of books that cover this

• Sharp: Steps in Commutative Algebra is similar too and perhaps a little easier then Atiyah & Mcdonald's book.
• Lang: Algebra looks a little bit into many areas of algebra.
• Matsumura: Commutative Ring Theory is pretty tough and pretty modern.

Answer 2

If you're just looking for the basics, then virtually any algebra book has the basics of these.

If you really need specifics, then Isaacs algebra book talks at length about Artinian and Noetherian rings.

For localization, any good commutative algebra book will do: Matsumura, Eisenbud, Lang, Grillet, Jacobson...

Answer 3

　Try Matsumura's "Commutative algebra"(note that this one is different from the book "Commutative Ring Theory"), however it's very advanced. For a more verbose approach, try "Commutative Algebra: with a view toward Algebraic Geometry" by Eisenbud, however I still thinking that Atiyah and Macdonald's book is one of the bests.

Answer 4

Algebra, Rings and Modules by Michiel Hazewinkel (et al.) is quite nice. It should cover everything you need and more.