= Generic-point embedding of regular functions
{title2=$\Gamma(U,\mathcal O_X)\hookrightarrow K(X)$}
On an <integral scheme> $X$, every nonempty open $U$ contains its <generic point> $\eta$. Taking a <germ> gives an injective <ring homomorphism> from its <regular functions> to the <function field> $\mathcal O_{X,\eta}$. Injectivity follows on each nonempty <affine open subscheme> from the injection of an <integral domain> into its <field of fractions>, and then from the <sheaf gluing axiom>. This lets regular functions on different open subsets be compared inside one field.
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