1) This might be a silly, but I don't know what it means when in the example after the proof of 5.7, when it says "we now have a ring that has Z2 as a subset." What exactly does this mean and why is it surprising? So surprising, that they say later, "However E does contain Z2 as an honest-to-goodness subset, without any identification." Also, what does it mean to say without any identification?
2) Arithmetic is more interesting in this congruence-class arithmetic. However, it still is very similar to the arithmetic that we learned in Zn.
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