Let K be a number field with unit rank at least four, containing a subfield M such that K/M is Galois of degree at least four. We show that the ring of integers of K is a Euclidean domain if and only ...

I'm looking for what the title says. Euclidean algorithm works and is fast for just a pair of numbers, but I don't see any obvious generalizations. A quick googling didn't turn up anything too ...