Let D be an integral domain with a multiplicative norm N such that N() 1 for D if and only if is a unit of D Show that every nonzero nonunit of D has a factorization into irreducibles in D

Question: Let D be an integral domain with a multiplicative norm N such that |N()| = 1 for D if and only if

Let D be an integral domain with a multiplicative norm N such that |N(α)| = 1 for α ∈ D if and only if α is a unit of D. Show that every nonzero nonunit of D has a factorization into irreducibles in D.

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