Niels Möller, On Schönhage's Algorithm and Subquadratic Integer GCD Computation, Mathematics of Computation, Vol. 77, No. 261 (Jan., 2008), pp. 589-607 ...

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 ...