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Math Help - Prime and Irreducible in Z[i]

  1. #1
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    Prime 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].
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    Assume that a = bc then N(a) = N(b)N(c) if N(a) is prime then one of N(b) or N(c) is 1 since the norm is 1 it means the element is a unit. And so b or c is a unit. Thus a is irreducible.
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