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Discussiones Mathematicae General Algebra and Applications 22(1) (2002) 25-31
DOI: https://doi.org/10.7151/dmgaa.1044

ON SOME FINITE GROUPOIDS WITH DISTRIBUTIVE SUBGROUPOID LATTICES

 Konrad Pióro

Institute of Mathematics, Warsaw University
Banacha 2, PL-02-097 Warsaw, Poland
e-mail: 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.

References

[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.

Received 20 October 2001