Lemma 41.19.1. Let $A$, $B$ be Noetherian local rings. Let $A \to B$ be a étale homomorphism of local rings. Then $\dim (A) = \dim (B)$.
Proof. See for example Algebra, Lemma 10.112.7. $\square$
Lemma 41.19.1. Let $A$, $B$ be Noetherian local rings. Let $A \to B$ be a étale homomorphism of local rings. Then $\dim (A) = \dim (B)$.
Proof. See for example Algebra, Lemma 10.112.7. $\square$
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