The Collaborative International Dictionary of English v.0.48:
Abbatial \Ab*ba"tial\ ([a^]b*b[=a]"shal), a. [LL. abbatialis : cf. F. abbatial.] Belonging to an abbey; as, abbatial rights. [1913 Webster]WordNet (r) 3.0 (2006):
abbatial adj 1: of or having to do with or belonging to an abbey or abbot, or abbess