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Prove that the ideal is prime in Z[x] but not maximal in
Chapter 17, Problem 32E(choose chapter or problem)
QUESTION:
Prove that the ideal \(\left\langle x^{2}+1\right\rangle\) is prime in Z[x] but not maximal in Z[x].
Questions & Answers
QUESTION:
Prove that the ideal \(\left\langle x^{2}+1\right\rangle\) is prime in Z[x] but not maximal in Z[x].
ANSWER:Step 1 of 2
Assume the following.
Then, we must have the following.
Since are all integers, we can take: