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.
- 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.
- 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?
- Any other suggestions/advices?
Thank you for your time.