Show that is a principal ideal domain.
I have already shown that is an integral domain. How do I show that all ideals are principal ( )?
Well, then you still can do something that is actually equivalent: show that the norm
in permits you to carry on "division with residue" just as the absolute value
allows us to do the same in the integers.
Once you have this proceed as with the integers to show the ring is a PID.
Tonio