2
$\begingroup$

Probably this is not a suitable question for this forum but I am stuck reading a paper in French and I cannot understand how "relever" is used in the following part of a theorem: We have that $f:A\mapsto B$ is an injective homomorphism.

$(i)$ Il existe un ideal maximal $\mathfrak{m}$ de $A$ tel que pour tout ideal premier $\mathfrak{p}$ de $A$, distincte de $\mathfrak{m}$, $A_{\mathfrak{p}}\mapsto B_{\mathfrak{p}}$ soit un isomorphisme.

$(ii)$ L'ideal maximal $\mathfrak{m}$ defini en $(i)$, se releve a $B$.

Can anyone help me explaining what that means?

$\endgroup$
7
  • $\begingroup$ I know translation-request tag is usually used to translate entire questions, but it really seems relevant here. $\endgroup$
    – rschwieb
    Dec 2 '13 at 14:24
  • $\begingroup$ Thanks, I didn't know that tag existed. $\endgroup$
    – user53970
    Dec 2 '13 at 14:24
  • 1
    $\begingroup$ @user53970: Ittay's answer seems OK but if you said what the object B was (giving more context) probably would help. Instead of "gives rise to B" I'm tempted to write "extends to B" but without knowing what B is this would be just a guess... $\endgroup$ Dec 2 '13 at 14:30
  • 2
    $\begingroup$ I think it's "The maximal ideal $\mathfrak{m}$ defined in $(i)$ lifts to $B$". But, context. $\endgroup$ Dec 2 '13 at 14:31
  • $\begingroup$ I added a little more context now. $\endgroup$
    – user53970
    Dec 2 '13 at 14:33
1
$\begingroup$

"The maximal ideal $m$ defined in (i), transfers [along $f:A\to B$] to $B$."

[It's a bit of a guess though (the last part of the sentence that is) since the context is missing. If you post a few more lines prior to that one, it will be easier to translate with more certainty.] * should be ok now *

Probably the exact meaning of that sentence is that the image $f(m)$ is an ideal in $B$.

$\endgroup$
5
  • $\begingroup$ Can you give it another try? I added a little more context. I understand the first sentence and most of the second sentence but I don't understand how "relever" is used in the second sentence. $\endgroup$
    – user53970
    Dec 2 '13 at 14:34
  • $\begingroup$ it would really help if you include the line where $B$ is defined (if it is defined). Releve in this context can mean 'gives rise to' or 'lifts to'. $\endgroup$ Dec 2 '13 at 14:35
  • $\begingroup$ I adjusted the translation and took some liberty to add some text between [...] that I hope clarifies things. $\endgroup$ Dec 2 '13 at 14:39
  • $\begingroup$ It is a little clearer now but not entirely clear. Can you expand a little more? What do you exactly mean by transfers to $B$? $\endgroup$
    – user53970
    Dec 2 '13 at 14:48
  • 1
    $\begingroup$ I wanted to make you know that you were exactly right. I checked with one of my professors and you were right. $\endgroup$
    – user53970
    Dec 2 '13 at 16:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.