Property of a euclidean map

Asked Aug 06 '13 at 07:08

Active Aug 06 '13 at 07:08

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Why an euclidean map defined onto a domain $R$, so a map $\delta\colon R\smallsetminus\{0\}\to\mathbb{N}$, satisfies $\delta(a)\leq\delta(ab)$ for every $a,b\in R\smallsetminus\{0\}$?

In some books, this property does not belongs to the definition of euclidean domain, and now I have to prove it.

asked Aug 06 '13 at 07:08

Martino

2

Consider the discussion of (EF2) here. – anon Aug 06 '13 at 07:11
@Lorenzo Since anon gave you the answer, maybe you can answer your own question and close it, for the record :) – Jonathan H Aug 06 '13 at 07:21
Ok, but I'm going to answer by copying what the link above says. I tried to do the euclidean division between $b$, $a$ and $ab$, but it does not work. – Martino Aug 06 '13 at 08:12
See my answer here – Tomas Aug 06 '13 at 08:14

Property of a euclidean map

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