The Munn representation of an inverse semigroup S, in which the semigroup is represented by isomorphisms between principal ideals of the semilattice E(S), is not always faithful. By introducing a concept of a presemilattice, Reilly considered of enlarging the carrier set E(S) of the Munn representation in order to obtain a faithful representation of S as an inverse subsemigroup of a structure resembling the Munn semigroup TE(S).
The purpose of this paper is to obtain a generalization of the Reilly's results for generalized inverse[*]-semigroups.