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Tag 05WQ

Chapter 10: Commutative Algebra > Section 10.150: Henselization and strict henselization

Lemma 10.150.10. Let $R$ be a local ring with henselization $R^h$. Let $I \subset \mathfrak m_R$. Then $R^h/IR^h$ is the henselization of $R/I$.

Proof. This is a special case of Lemma 10.150.9. $\square$

    The code snippet corresponding to this tag is a part of the file algebra.tex and is located in lines 41072–41077 (see updates for more information).

    \begin{lemma}
    \label{lemma-quotient-henselization}
    Let $R$ be a local ring with henselization $R^h$.
    Let $I \subset \mathfrak m_R$.
    Then $R^h/IR^h$ is the henselization of $R/I$.
    \end{lemma}
    
    \begin{proof}
    This is a special case of
    Lemma \ref{lemma-quasi-finite-henselization}.
    \end{proof}

    Comments (1)

    Comment #2805 by Minseon Shin on September 13, 2017 a 9:04 pm UTC

    Suggested slogan: Henselization is compatible with quotients.

    There are also 2 comments on Section 10.150: Commutative Algebra.

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