uniqueness Euclidean Norm in Euclidean domain

Question

Let $R$ be a Euclidean domain with the euclidean norm $N$. Is $N$ unique?

Is there any trivial counterexample? or is that statement is somehow true?

At least, there are different Euclidean functions in general, see http://math.stackexchange.com/questions/763043/what-euclidean-functions-can-the-ring-of-integers-be-endowed-with/763428#763428. — Dietrich Burde, Sep 08 '14 at 13:58

score 0 · Answer 1 · edited Jan 21 '17 at 21:59

0

I Found a counter example:

For the ring of polynomials, we can take $N_1(p)=\deg(p)$ and $N_2(p)=2^{\deg(p)}$.

edited Jan 21 '17 at 21:59

user26857

answered Sep 08 '14 at 14:04

Snufsan

1 Answers1