Question: If A is a unique factorization domain, show that A is normal ? Show an example of an integral extension of rings A ⊂ B, such that A is a field and B is not an integral domain (cf. Lemma)
Lemma: Let A ⊂ B be a ring extension. If B is a domain and b ∈ B is integral over A, then A[b] is a field if and only if A is a field.