The concepts really aren't too difficult to understand, I'm just concerned that the application will be more difficult than it seems. Generally (and this section is no exception), I have to break down each theorem into it's individual parts and think "ok, so if a subring I of R is an ideal, then there's an element of R and an element of I, and when I multiply them together the product is in I. Ok, that makes sense."
Reflective:
I thought it was really cool when they talked about how the congruence modulo 3 can be characterized as a-b being a multiple of 3. It's really the same thing we've said all along, but either they haven't phrased it that way, or I missed it when they did. That definition makes a lot more sense in my mind than saying that 3 divides a-b.
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