Etymology
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prefecture (n.)

"administrative district, office, or jurisdiction of a prefect," mid-15c., from Old French préfecture (13c.) and directly from Latin praefectura, or assembled locally from prefect + -ure. Also used as the English equivalent to Chinese fu, "an administrative division consisting of several districts" (1885). 

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Definitions of prefecture

prefecture (n.)
the district administered by a prefect (as in France or Japan or the Roman Empire);
prefecture (n.)
the office of prefect;
From wordnet.princeton.edu