Euclidean ring (redirected from Euclidean domain)

Euclidean ring [yü‚klid·ē·ən ′riŋ]

(mathematics)

A commutative ring, together with a function, ƒ, from the nonzero elements of the ring to the nonnegative integers, such that (1) ƒ(xy) ≥ ƒ(x) ifxy≠ 0, and (2) for any members of the ring,xandy, withx≠ 0, there are membersqandrsuch thaty=qx+rand eitherr=0 orf(r)<f(x).