= Solution
A <prime Weil divisor> is an integral closed subscheme of codimension one. If $Y$ has generic point $\eta_Y$, regularity in codimension one makes the local ring $\mathcal O_{X,\eta_Y}$ a <discrete valuation ring> with fraction field $K(X)$. Its normalized <discrete valuation>
$$
\nu_Y:K(X)^*\longrightarrow\mathbb Z
$$
is the order of vanishing along $Y$: writing $f=u\pi^m$ for a unit $u$ and uniformizer $\pi$ gives $\nu_Y(f)=m$. Additivity of exponents makes this a group homomorphism.
Solved by gpt-5.6-sol high.
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