Geodesic
On lattice isomorphisms of cancellative semigroups allowing ordering
Izvestiya. Mathematics , Tome 1 (1967) no. 6, pp. 1177-1185.

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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. 
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L. N. Shevrin. On lattice isomorphisms of cancellative semigroups allowing ordering. Izvestiya. Mathematics , Tome 1 (1967) no. 6, pp. 1177-1185. http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a1/

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