Geodesic
Lattices Embeddable in Subsemigroup Lattices. II. Cancellative Semigroups
Algebra i logika, Tome 45 (2006) no. 4, pp. 436-446

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Repnitskii proved that any lattice embeds in a subsemigroup lattice of some commutative, cancellative, idempotent free semigroup with unique roots. In that proof, use is made of a result by Bredikhin and Schein stating that any lattice embeds in a suborder lattice of suitable partial order. Here, we present a direct proof of Repnitskii's result which is independent of Bredikhin–Schein's, thus giving the answer to the question posed by Shevrin and Ovsyannikov.
Keywords: commutative semigroup, subsemilattice lattice. 
@article{AL_2006_45_4_a3,
     author = {M. V. Semenova},
     title = {Lattices {Embeddable} in {Subsemigroup} {Lattices.} {II.} {Cancellative} {Semigroups}},
     journal = {Algebra i logika},
     pages = {436--446},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_4_a3/}
}
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M. V. Semenova. Lattices Embeddable in Subsemigroup Lattices. II. Cancellative Semigroups. Algebra i logika, Tome 45 (2006) no. 4, pp. 436-446. http://geodesic.mathdoc.fr/item/AL_2006_45_4_a3/