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 ...

Huguette NAPIAS, A generalization of the LLL-algorithm over euclidean rings or orders, Journal de Théorie des Nombres de Bordeaux, Vol. 8, No. 2 (1996), pp. 387-396 ...