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Discuss the properties of unique factorization domain

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Reference no: EM131586705

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.

Reference no: EM131586705

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