Abstract:
The article contains a description of semigroups lattice-isomorphic to cancellative semigroups allowing positive ordering, and indicates the type of mapping inducing any lattice isomorphism of a cancellative semigroup allowing positive ordering. Various corollaries of the basic result are listed; in particular, it is shown that the study of lattice isomorphism of arbitrary cancellative semigroups allowing ordering reduces entirely to the case of semigroups without identity.