Thomas Koshy, 80.48 The Euclidean Algorithm via Matrices and a Calculator, The Mathematical Gazette, Vol. 80, No. 489 (Nov., 1996), pp. 570-574 ...

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 ...