Let D be a Euclidean domain values? (That is, must the range of v be infinite?) Let D be a Euclidean domain values? (That is, must the range of v be infinite?)

Question

Question

Let D be a Euclidean domain values? (That is, must the range of v be infinite?)

math Advanced-Math

Answer 1

Answer #1

Need not be.

The simplest example is a trivial Euclidean valuation. It defined as

$\newline \nu:D^*\to \mathbb N \newline \newline \nu(x)=0 \forall x\in D^*$

It is easy to check that it is valuation with range singleton set.

Answer 2

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