4.II.11C
Let be the ring of Gaussian integers , where , which you may assume to be a unique factorization domain. Prove that every prime element of divides precisely one positive prime number in . List, without proof, the prime elements of , up to associates.
Let be a prime number in . Prove that has cardinality . Prove that is not a field. If , show that is a field. If , decide whether is a field or not, justifying your answer.
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