Difficult: The hardest part of this section for me to understand was exactly how to determine that a quotient ring is a field. I understand how to prove that something is a field in general, but in the book, the author assumes that if a ring is isomorphic to a field, it is also a field. Did we come to this conclusion before? We probably did, but it was confusing to me while I read because it was stated without any reasoning. It would help me to see and talk about some examples in class.
Reflective: Primes have always interested me, and I think that it is really interesting that we can extend the idea of a prime to ideals. It makes sense, and I think it is amazing that prime numbers have so many applications. I want to know more, though. Why does understanding about prime ideals help us? I know it must have some important application or reason, but right now we are just learning it. I wonder what prime ideals tell us.
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