Answer to Question #89033 in Abstract Algebra for rahul

Question

Let N ∈d , where d ≠1 and d is not divisible by the square of a prime. Prove that N:Z[square root of d] maps N union {0} : N(a+b sqr root d) = |a^2 -db^2| satisfies the following properties for x,y belongs to Z[sqr root d].

1. N(x) = 0 if x=0.
2 N(xy) = N(x)N(y)
3. N(x) =1 if x is a unit
4. N(x) is prime if x is irreducible.

Answer 1

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