Definition 29.44.1. Let $f : X \to S$ be a morphism of schemes.

1. We say that $f$ is integral if $f$ is affine and if for every affine open $\mathop{\mathrm{Spec}}(R) = V \subset S$ with inverse image $\mathop{\mathrm{Spec}}(A) = f^{-1}(V) \subset X$ the associated ring map $R \to A$ is integral.

2. We say that $f$ is finite if $f$ is affine and if for every affine open $\mathop{\mathrm{Spec}}(R) = V \subset S$ with inverse image $\mathop{\mathrm{Spec}}(A) = f^{-1}(V) \subset X$ the associated ring map $R \to A$ is finite.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).