Geodesic
Representation of lattices by congruence lattices of semigroups without idempotents
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 208-217 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 the congruence lattice of some semigroup without idempotents. This implies that every distributive algebraic lattice with at most countably many compact elements is also representable as the congruence lattice of a semigroup without idempotents.
Keywords: congruence lattice, semigroup, representation of lattices. 
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A. L. Popovich. Representation of lattices by congruence lattices of semigroups without idempotents. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 208-217. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a24/

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