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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.

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4 Answers

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　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.

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There are plenty of books that cover this

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I've found that Sharp's book is very verbose, sometimes to a fault. There's a nice median somewhere in between Atiyah & Macdonald and Sharp that I've yet to see in a commutative algebra book. – JSchlather Feb 1 at 19:37
@JacobSchlather Yes, that might be the case but on the other hand there are also fresher materials in Sharps book. I like all of the above books for different reasons. – AD. Feb 2 at 7:41
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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...

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

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