Difficult: I had a hard time understanding what maximal ideals are. I think that maybe it is notation that is confusing me, but I just couldn't quite understand what it means for an ideal to be maximal. As I was reading the definition, I also realized that I'm not really sure what it means for two ideals to be equal. So I don't know how to go about proving something is maximal. Mostly because I'm not sure how to prove that two ideals are equal.
Connections: I like dealing with prime numbers, or concepts having to do with primes. I think that things that are prime have very nice properties and are really nice to work with. Some of the examples were pretty simple, so I think for the most part I understood them. However, sometimes I think I understand things and I try to do the homework and I'm not quite sure how to apply things. So hopefully applying the concepts of prime ideals will be something I will be able to work with, and I will be able to understand how to use information about ideals being prime help me out in some of the proofs.
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