Difficult:
Like last time, I found the material too intuitive to really follow the formalism of the proofs. The danger in this is made apparent by example 4.9.3, where Q is adjoined by the cube root of 3. Without such a formalism to use, patterns found to work for other subfields would be assumed to work for any subfield without proof, which is show to be false in this example.
Reflective:
It is interesting that the definition for a field extension used the language of monomorphisms rather than superfields. It mentions that this is for technical reasons, but I would be most interested to see what they are. I would assume that at some point we step away from using a subfield of C to define field extensions at some point, and use formal roots that are assumed to exist instead, like was done in Math 371.
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