I had a few quick Quadratic Field related problems I wanted to throw out there to see if someone can give me a hand with.
1 - Does anyone know of a Quadratic Integer in Q[Sqrt(-1)] that is prime but whose norm is not prime?
If by "quadratic integer" you meant "Gaussian integer" or just "integer", then the only primes in are elements of the form , with an ordinary prime in , or elements of the form , with a rational prime, and the prime .
It's easy to check all these primes have a prime norm, so...
2 - What is a prime factorization of 6 in Q[Sqrt(-1)] ? I have been having trouble understanding these.
, with a unit, of course.
Thank you! -Samson