Geodesic
Half-isomorphisms of cancellative semigroups
Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 915-921.

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It is proved in this article that every half-isomorphism of a cancellative semigroup onto an arbitrary semigroup is either an isomorphism or an anti-isomorphism. 
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L. N. Shevrin. Half-isomorphisms of cancellative semigroups. Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 915-921. http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a0/

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