On some finite groupoids with distributive subgroupoid lattices

• Autorzy: Konrad Pióro
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

groupoid; subgroupoid lattice; distributive lattice

Kategorie tematyczne

• 20N02: Sets with a single binary operation (groupoids)
• 06B15: Representation theory
• 06D05: Structure and representation theory
• 08A30: Subalgebras, congruence relations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 25-31

Daty

wydano

2002

otrzymano

2001-10-20

Twórcy

autor

Konrad Pióro

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgaa.1044