 The first example of a Euclidean domain that was not norm-Euclidean (with ) was published in 1994.In 1973, Weinberger proved that a quadratic integer ring with is Euclidean if, and only if, it is a principal ideal domain, provided that the generalized Riemann hypothesis holds.The Euclidean algorithm may be applied to some noncommutative rings such as the set of Hurwitz quaternions.