1) I guess they just didn't go through a ton of the proofs of theorem 4.1 and I'm just wondering if we are going to go through those in class? I think for the most part proofs involving polynomials aren't very difficult, per say, but more tedious. But because there are so many variables and constants going on, I do get a little bit confused. Also, why does it help us to know what the degree of the polynomial is?
2) I thought it was interesting that you could take any ring R (even if it is not a commutative ring) and there exists a ring P that looks like it does have commutativity, looking at the second part of theorem 4.1.
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