The Priory reference article from the English Wikipedia on 24-Apr-2004
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Priory

A priory is a monastery governed by a prior or prioress. An alien priory is a priory which is dependent on a foreign mother house, and an alien priory cell was a residence of two or three monks dependent on a foreign mother house but sent to exploit a distant estate. Alien priory cells were suppressed in 1414.

Strictly speaking, a priory is a secondary house created by an existing abbey, but this distinction fell out of use in late mediaeval times.