Difficult: I felt like in this section I understood the idea of ideals, until it started talking about the different kinds of ideals. I really liked theorem 6.1, and I thought it was pretty straight-forward. However, the principal ideals, and finitely generated ideals were a little confusing to me. I wasn't quite sure what the difference was between them, and how they differed from just being an ideal. I found it difficult to distinguish between them and understand why they were important.
Connections: As I mentioned before, I liked the idea of the ideals in the beginning. I felt like it sounded very familiar to stuff we have already learned this semester. Theorem 6.1 reminded me a lot of a subring! The properties to be an ideal seem to me to be a lot like the properties to be a subring. I like that the properties of being an ideal are that they are closed under subtraction and multiplication, even though it is a little different from a subring since in the multiplication, one of the elements need not be in the set I, but the product of an element from within the set and outside the set need only be in I.
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