Part I: What was the most difficult part of the material for you?
I am most confused about the definition of an extension field and a subfield. With how they used subfield, I felt like it should have been used the other way, like K is a subfield of F. And so that is why I am even more confused with the extension field definition. It doesn't make sense to me with how it has been for subrings.
Part II: Write something reflective about the reading.
At first I thought it would be too obvious to say that F[x]/p(x) is a field if p(x) is irreducible because F[x] comes from a field, but then I realized I was generalizing too much. Even though F is field, I guess it is still possible that F[x]/p(x) is not a field when p(x) is reducible, which is really crazy.
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