I think the most difficult part of this section was when it started discussing constructing a ring by identifying a F with it's copy F* inside F[x]/(p(x)). I don't know what identifying means. I don't know how they got from one thing to another in that example on page 126 with the addition and multiplication tables. I also didn't understand why x^2-2 and 2x+5 are relatively prime as in the example on page 127 and how I should know this based off of information from the top of my head. I think I'm starting to fall behind in my understanding of the things we are discussing and each section is getting more and more confusing for me. I need to reread everything from chapter 4 I think.
I don't understand how they constructed a ring containing a subset isomorphic to Z2 but I think it is very interesting that that can be done with any field and a nonconstant polynomial. I am also relieved that addition and multiplication work the same way for congruence classes in polynomial rings. I would have dreaded it if they had had special rules.
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