Lemma 10.61.3. Let $S$ be a nonzero finite type algebra over a field $k$. The following are equivalent

$\dim (S) = 0$,

$S$ has finitely many primes,

$S$ has finitely many maximal ideals,

$\mathop{\mathrm{Spec}}(S)$ satisfies one of the equivalent conditions of Lemma 10.26.5, and

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## Comments (2)

Comment #6269 by Henry West on

Comment #6270 by Henry West on