From the definition of discrete valuation, can we conclude that $v|_{K^*}$ is surjective?
2026-03-25 22:23:54.1774477434
Can we conclude that $v|_{K^*}$ is surjective?
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If $v$ is a valuation, so is $k v$ for any $k\in\mathbf{N}^*$, so there's no chance a valuation is necessarily surjective.