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Tag 00HR

Chapter 10: Commutative Algebra > Section 10.38: Flat modules and flat ring maps

Lemma 10.38.17. A flat local ring homomorphism of local rings is faithfully flat.

Proof. Immediate from Lemma 10.38.16. $\square$

    The code snippet corresponding to this tag is a part of the file algebra.tex and is located in lines 8815–8818 (see updates for more information).

    \begin{lemma}
    \label{lemma-local-flat-ff}
    A flat local ring homomorphism of local rings is faithfully flat.
    \end{lemma}
    
    \begin{proof}
    Immediate from Lemma \ref{lemma-ff-rings}.
    \end{proof}

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