Definition 10.121.2. Suppose that $K$ is a field, and $R \subset K$ is a local^{1} Noetherian subring of dimension $1$ with fraction field $K$. In this case we define the *order of vanishing along $R$*

by the rule

if $x \in R$ and we set $\text{ord}_ R(x/y) = \text{ord}_ R(x) - \text{ord}_ R(y)$ for $x, y \in R$ both nonzero.

## Comments (0)

There are also: