Question

Is d function in euclidian ring is a incresing function?

Answer 1

n. ... Any function d: R−{0} → N that satisfies (1.1) will be called aEuclidean function on R. Thus aEuclidean domain in Definition 1.2 is an integral domain that admits aEuclidean function, while a Euclideandomain in Definition 1.1 is an integral domain that admits a Euclidean function satisfying the d-inequality.