Difficult:
I thought the most difficult part of this section was keeping track of all the different types of rings. I had a hard time distinguishing when a ring is commutative, is a ring with identity. And then once I figure out if its commutative, then it could be an integral domain or a field. I didn't really understand these definitions and how best to keep track of them. I also didn't really understand what the 0 with a subscript R meant, or a 1 with subscript R. I think in this section I mostly got lost in all the definitions and new notation.
Connection:
As with modular arithmetic, I like that rings follow properties of addition and multiplication like the integers. It makes it easier for me when I already understand the axioms that define a ring. So once I can better understand the new notation, I will feel more comfortable with recognizing rings because I already know about the axioms, since I have been using these axioms pretty much all of my life.
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