1. The second half of this section was rather short so I did not have much that I didn't understand. If I had to choose something though, it would have to be where it introduces subrings - part iv of Theorem 3.2 - where it says we have to show that the solution has to be an element of the set S, which I am not quite sure how to prove. Also, I do not know what a field is.
2. I thought it was interesting that they introduced something called "subrings". I know what sets are; I know what subsets are. I know what rings are; I am learning what a subring is. There are similar correlations between subsets and subrings, and it is interesting to see the comparison.
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