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ArticleOriginal scientific text

Title

On some finite groupoids with distributive subgroupoid lattices

Authors 1

Affiliations

  1. Institute of Mathematics, Warsaw University, Banacha 2, PL-02-097 Warsaw, Poland

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

ENG
groupoid, subgroupoid lattice, distributive lattice

Bibliography

  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.
Discussiones Mathematicae - General Algebra and Applications
2002/22/1
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Pages:
25-31
Main language of publication
English
Received
2001-10-20
Published
2002

DOI: 10.7151/dmgaa.1044

Exact and natural sciences