The Collaborative International Dictionary of English v.0.48:

Minster \Min"ster\, n. [AS. mynster, fr. L. monasterium. See
   Monastery.] (Arch.)
   A church of a monastery. The name is often retained and
   applied to the church after the monastery has ceased to exist
   (as Beverly Minster, Southwell Minster, etc.), and is also
   improperly used for any large church.
   [1913 Webster]

   Minster house, the official house in which the canons of a
      cathedral live in common or in rotation. --Shipley.
      [1913 Webster]