Let $k$ be a field, let $X$ be an irreducible affine variety over $k$, and let $A=k[X]$ be its coordinate ring. Suppose there exist algebraically independent elements $y_1,\dots,y_d\in A$ such that the inclusion
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\begin{align*}
k[y_1,\dots,y_d]\subset A
\end{align*}
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makes $A$ a finite module over the polynomial subring $k[y_1,\dots,y_d]$. With the convention that
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\begin{align*}
\dim X=\dim A
\end{align*}
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is the Krull dimension of the coordinate ring, one has