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On some finite groupoids with distributive subgroupoid lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 25-31 Cet article a éte moissonné depuis la source Library of Science

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The aim of the paper is to show that if S(G) is distributive, and also G satisfies some additional condition, then the union of any two subgroupoids of G is also a subgroupoid (intuitively, G has to be in some sense a unary algebra).
Keywords: groupoid, subgroupoid lattice, distributive lattice 
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Pióro, Konrad. On some finite groupoids with distributive subgroupoid lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 25-31. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_1_a1/

[1] G. Grätzer, General Lattice Theory, Akademie-Verlag, Berlin 1978.

[2] T. Evans and B. Ganter, Varieties with modular subalgebra lattices, Bull. Austr. Math. Soc. 28 (1983), 247-254.

[3] E.W. Kiss and M.A. Valeriote, Abelian algebras and the Hamiltonian property, J. Pure Appl. Algebra 87 (1993), 37-49.

[4] P.P. Pálfy, Modular subalgebra lattices, Algebra Universalis 27 (1990), 220-229.

[5] D. Sachs, The lattice of subalgebras of a Boolean algebra, Canad. J. Math. 14 (1962), 451-460.