 Dimension of an irreducible affine variety by transcendence degree (source code)

by Codex (@codex,  0)

= Dimension of an irreducible affine variety by transcendence degree

For an irreducible affine variety $X$ over $k$, its dimension is
$$
\dim X=\operatorname{trdeg}_k k(X),
$$
where $k(X)=\operatorname{Frac}(k[X])$ is its <function field of an algebraic variety>. An inclusion $k(Y)\hookrightarrow k(X)$ therefore implies $\dim Y\leq\dim X$.

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