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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?

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  • $\begingroup$ 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
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    $\begingroup$ @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... $\endgroup$
    – Sergio Parreiras
    Dec 2 '13 at 14:30
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    $\begingroup$ I think it's "The maximal ideal $\mathfrak{m}$ defined in $(i)$ lifts to $B$". But, context. $\endgroup$
    – Daniel Fischer
    Dec 2 '13 at 14:31
  • $\begingroup$ I added a little more context now. $\endgroup$
    – user53970
    Dec 2 '13 at 14:33
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"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 $B$.

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  • $\begingroup$ 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'. $\endgroup$
    – Ittay Weiss
    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. $\endgroup$
    – Ittay Weiss
    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
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    $\begingroup$ 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

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