# Integral k-scheme of locally finite type

An integral scheme of locally finite type over a field is always of finite type of the field?

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No, take an infinite disjoint union of $\mathrm{Spec}(k)$. if it is not supposed to be separated. Just glue infinitely many copies of affines lines $\mathbb A^1$ along $\mathbb A^1\setminus \{ 0\}$.
Now even if $X$ is integral and separated, this is not necessarily true. See this example of BCnrd at mathoverflow.