Let a be in Z[i], show that if N(a) is prime in Z, then a is irreducible in Z[i].

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- Jan 17th 2008, 07:55 PMtttcomraderPrime and Irreducible in Z[i]
Let a be in Z[i], show that if N(a) is prime in Z, then a is irreducible in Z[i].

- Jan 17th 2008, 08:09 PMThePerfectHacker
Assume that then if is prime then one of or is since the norm is it means the element is a unit. And so or is a unit. Thus is irreducible.