# Translate a sentence (regarding rings and maximal ideals) from french

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?

• I know translation-request tag is usually used to translate entire questions, but it really seems relevant here. Dec 2, 2013 at 14:24
• Thanks, I didn't know that tag existed. Dec 2, 2013 at 14:24
• @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... Dec 2, 2013 at 14:30
• I think it's "The maximal ideal $\mathfrak{m}$ defined in $(i)$ lifts to $B$". But, context. Dec 2, 2013 at 14:31
• I added a little more context now. Dec 2, 2013 at 14:33

"The maximal ideal $m$ defined in (i), transfers [along $f:A\to B$] to $B$."
Probably the exact meaning of that sentence is that the image $f(m)$ is an ideal in $B$.
• 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'. Dec 2, 2013 at 14:35
• It is a little clearer now but not entirely clear. Can you expand a little more? What do you exactly mean by transfers to $B$? Dec 2, 2013 at 14:48