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