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I have studied about Group, Ring, Field, Galois theory (a little), and I am interested in them. As I understand, they maybe belong to Commutative algebra, right? If yes, I want to follow this direction. What subjects do I need study in order to continue to higher study in this domain? (I though this may be the only way I could go. Now, I am also studying some subjects, such as differential geometry, and I feel really tired.)

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    None of them (except for fields) belong to commutative algebra (unless explicitely stated). And if you wish to study it further well, you know, there are books, internet, universities. I'm not really sure what exactly is your problem and how we can help you? – freakish Jul 05 '17 at 10:01
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    My problem is that I will have to choose a subject to do an undergraduate thesis (or memoir), and I want to look for a direction, to prepare now. –  Jul 05 '17 at 10:06
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    Right, now I understand. Well, it's hard to answer such question. This totally depends on your preferences. I think you should talk with your teachers/mentors (someone that knows you better) and ask them for guidance. – freakish Jul 05 '17 at 10:16
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    I agree with freakish. Furthermore it seems logical to me that the next step for you would be to look into "field theory for rings" i.e. modules. Many of the concepts are simmilar to those in field theory and linear algebra as they are a generalization. – user424862 Jul 05 '17 at 10:49

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