I don't understand their example at the top of pg 155. They say that the principle ideal (x) in Z[x] is prime, but since the quotient ring Z[x]/(x) is isomorphic to Z, then Z[x]/(x) is an integral domain but not a field. How does that isomorphism make it so that it can't be a field?
Reflective:
I think the definition (and explanation) of a prime ideal was the only thing that made complete sense in this chapter. It made logical sense to me to go from saying that when p|bc then p|b or p|c to saying when bc is in (p) then either b is in (p) or c is in (p).
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