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In this semester, I'm doing a project in Algebra, and I would like take some advices and suggestions. To be more precise, I will study the Cohen-Macaulay Orders and modules in relation to the Krull dimension.

Before my questions, I should inform you that I'm in the last undergraduate year of my studies, and so I have attented Basic Algebra, Group Theory, Galois Theory and Number Theory.

So far, I have studied some commutative algebra: Modules, Noetherian Modules, Noetherian Rings and Algebras. I used several sources but mostly Dummit's and Foote's "Abstract Algebra", Rotman's "Advanced Modern Algebra", Lovett's "Abstract Algebra, Structures and Applications" and Atiyah's & Macdonald's "Introduction to Commutative Algebra". Also, I found really usefull Conrad's Expository Papers. But, my basis for the topics above is D & F.

Questions.

  1. Could you please recommend me some (combination, probably, of) good books/notes? Any exercise books? Please, keep in mind that I working mostly myself, so I'm looking for good books with thorough analysis of each proof, example etc., many examples and good exercises to solve, suitable for self-study and for the first touch in the subject.
  2. Do you believe that the "general" abstract algebra books are suitable for this purpose, or someone should study from more specialized books, in order to focus on these topics?
  3. Any other suggestions/advices?

Thank you for your time.

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    $\begingroup$ If you're looking for background on Cohen-Macaulay rings, Ch. 18 of Eisenbud's commutative algebra book might be useful. $\endgroup$ – André 3000 Dec 10 '18 at 1:51
  • $\begingroup$ @André3000 Thank you for your comment and sorry for the delay. Ok, I ll check! $\endgroup$ – Chris Dec 12 '18 at 0:14
  • $\begingroup$ Any other comments/answers please? $\endgroup$ – Chris Dec 12 '18 at 0:44

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