I'm looking for a DVR which does not contain $\mathbb{Z}$ as a set.
N.B Here, I assume character of DVR is zero. In character $0$ , there are easy counter examples.
All DVR I know seems to contain $\mathbb{Z}$, and valuation on it, I saw notation like $v(n)$, where $n$ is integer.
With a tacit understanding, it seems domain field of $v$ contains $\mathbb{Z}$.
Where am I missing?
Thank you in advance.