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Tag 03QJ

Chapter 53: Étale Cohomology > Section 53.32: Henselian rings

Lemma 53.32.5. If $R$ is henselian and $A$ is a finite $R$-algebra, then $A$ is a finite product of henselian local rings.

Proof. See Algebra, Lemma 10.148.4. $\square$

    The code snippet corresponding to this tag is a part of the file etale-cohomology.tex and is located in lines 4150–4154 (see updates for more information).

    \begin{lemma}
    \label{lemma-finite-over-henselian}
    If $R$ is henselian and $A$ is a finite $R$-algebra, then $A$ is a finite
    product of henselian local rings.
    \end{lemma}
    
    \begin{proof}
    See
    Algebra, Lemma \ref{algebra-lemma-finite-over-henselian}.
    \end{proof}

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