Translational hull of an inverse semigroup

The theory of ideal extensions of semigroups is dependent upon adequate knowledge of the translational hull. We characterize here certain basic structures in the translational hull, Ω(S), of an arbitrary inverse semigroup S: in particular, the semilattice of idempotents of Ω(S) and the group of units of Ω(S). An isomorphic copy of each of these structures is given in terms of the semilattice of idempotents of S.