I am an undergraduate in my last semester, and due to bureaucratic reasons I couldn't take a course in Ring Theory until now. Again, for bureaucracy, I had to enroll in a course in Field theory and Galois theory this quarter, and I will be taking the Rings course in the next one. Not the ideal situation, I know, but that's how things ended up being and I won't be able to change the order in which I will take the courses (I tried to). So, I need to know what's the basic results of Ring theory I should be at least know to enunciate/or know the proofs in order to follow this course in field theory, as I listened that it is a very deep subject and I'm concerned about my ability to survive it. I didn't took the course in Ring theory but studied something by myself in the last month, so I know the language of homomorphisms, polynomial rings and the abstract Chinese Remainder Theorem, but I would like to know what exactly is demanded. Also, which book is a good reference to study field theory in a first course, given the present situation?
2026-03-25 09:50:12.1774432212
Minimal of Ring Theory for Field/Galois theory.
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