Geodesic
On the representation of lattices by congruence lattices of semigroups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 199-208

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It is proved that every distributive algebraic lattice such that its compact elements form a lattice with unit can be represented as a congruence lattice for an appropriate semigroup.
Keywords: algebraic lattice, distributive lattice, congruence lattice, semigroup. 
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A. L. Popovich; V. B. Repnitskii. On the representation of lattices by congruence lattices of semigroups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 199-208. http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a17/