The Stacks Project


Tag 08WP

Chapter 34: Descent > Section 34.4: Descent for universally injective morphisms

Lemma 34.4.8. Any faithfully flat ring map is universally injective.

Proof. This is a reformulation of Algebra, Lemma 10.81.11. $\square$

    The code snippet corresponding to this tag is a part of the file descent.tex and is located in lines 927–930 (see updates for more information).

    \begin{lemma}
    \label{lemma-faithfully-flat-universally-injective}
    Any faithfully flat ring map is universally injective.
    \end{lemma}
    
    \begin{proof}
    This is a reformulation of Algebra, Lemma
    \ref{algebra-lemma-faithfully-flat-universally-injective}.
    \end{proof}

    Comments (0)

    There are no comments yet for this tag.

    There are also 3 comments on Section 34.4: Descent.

    Add a comment on tag 08WP

    Your email address will not be published. Required fields are marked.

    In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the lower-right corner).

    All contributions are licensed under the GNU Free Documentation License.




    In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following box. So in case this where tag 0321 you just have to write 0321. Beware of the difference between the letter 'O' and the digit 0.

    This captcha seems more appropriate than the usual illegible gibberish, right?