Discussiones
Mathematicae General Algebra and Applications 22(1) (2002) 2531
doi: 10.7151/dmgaa.1044
ON SOME FINITE GROUPOIDS WITH DISTRIBUTIVE SUBGROUPOID LATTICES
Konrad Pióro
Institute of Mathematics, Warsaw University
Banacha 2, PL02097 Warsaw, Poland
email: kpioro@mimuw.edu.pl
Abstract
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.
2000 AMS Mathematics Subject Classifications: 20N02, 08A30, 06B15, 06D05.
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D. Sachs, The lattice of subalgebras of a Boolean algebra, Canad. J. Math. 14 (1962),
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Received 20 October 2001