Definition 41.3.1. Let $A$, $B$ be Noetherian local rings. A local homomorphism $A \to B$ is said to be unramified homomorphism of local rings if

1. $\mathfrak m_ AB = \mathfrak m_ B$,

2. $\kappa (\mathfrak m_ B)$ is a finite separable extension of $\kappa (\mathfrak m_ A)$, and

3. $B$ is essentially of finite type over $A$ (this means that $B$ is the localization of a finite type $A$-algebra at a prime).

Comment #54 by Rankeya on

I think in (2) you want $\kappa(\mathfrak m_B)$ to be a finite separable extension of $\kappa(\mathfrak m_A)$.

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