Let
R be a
commutative integral domain. We say that
R is a
Euclidean ring (or ER) if there exists a
function
d: R\{0} ->N (to the natural numbers) (usually called
a
norm such that
- if a,b are nonzero elements of R then
d(ab)>=d(a)
- Let a,b in R with a nonzero. Then
there exists q,r in R such that
b=qa+r with either r=0 or d(r)<d(a)
Examples