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Die Lehrer freuen sich über den Erfolg ihrer Studenten.

What I don't understand about this sentence is, den Erfolg is accusative but then why Studenten takes ihrer, dative? I know that ihrer here is a pronoun but why is it not ihre Studenten, why not accusative? Is it about über, but if so how can I understand which object takes accusative and which one takes dative?

Thank you for your help.

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    ihrer is in fact genitive – tofro Jul 28 '17 at 20:26
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    "über" causes "den Erfolg" to be accusative. "Ihrer Studenten" is genitive, because "der Erfolg" is owned by the students. Whose success? Genitive. – gnasher729 Jul 28 '17 at 21:12
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I'm writing an answer even though the comments essentially already answered this. But it's still listed as unanswered.

Über takes the accusative: “Freuen sich über wen? – Den Erfolg.” (Happy about whom or what?)

But that Erfolg is further described using a genitive: “Wessen Erfolg? – Den ihrer Studenten.” (Whose success?)

You could conceivably say “Die Lehrer freuen sich über ihre Studenten und deren Erfolg.” This would be using accusative with both objects. But it has a slightly different meaning, as it implies the teachers being happy about their students by themselves, not only about their success.

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