Hello,

let be a primitive fifth root of unity and the ring of integers in .

How to prove, that is a prime ideal in ?

I know that is a dedekind ring and therefore each ideal has a factorization in prime ideals and furthermore i know that the ring of integers of is if and if .

In the case of it is easy because of

and .

But and now i can't simplify the term and i don't know how the ring looks like if .

Please help me.

Bye,

Alexander