Geodesic
Representation of distributive algebraic spatial lattices by congruence lattices of semigroups and groupoids
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 818-831

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We prove that every distributive algebraic spatial lattice is isomorphic to the congruence lattice of some semigroup and also of some groupoid with zero satisfying identities $x^2=0$ and $xy=yx$.
Keywords: congruence lattice, semigroup, spatial lattice.
Mots-clés : groupoid 
@article{SEMR_2015_12_a27,
     author = {A. L. Popovich},
     title = {Representation of distributive algebraic spatial lattices by congruence lattices of semigroups and groupoids},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {818--831},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a27/}
}
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A. L. Popovich. Representation of distributive algebraic spatial lattices by congruence lattices of semigroups and groupoids. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 818-831. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a27/