Lemma 10.9.16 (02C9)—The Stacks project

Processing math: 100%

Ideals in the localization of a ring are localizations of ideals.

Lemma 10.9.16. Each ideal $I'$ of $S^{-1}A$ takes the form $S^{-1}I$ , where one can take $I$ to be the inverse image of $I'$ in $A$ .

Proof. Immediate from Lemma 10.9.15. $\square$

Comments (1)

Comment #841 by Johan Commelin on July 24, 2014 at 18:36

Suggested slogan: Ideals in the localization of a ring are localizations of ideals.

There are also:

7 comment(s) on Section 10.9: Localization

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 toolbar).

Comments (1)

Post a comment