On some finite groupoids with distributive subgroupoid lattices
Discussiones Mathematicae - General Algebra and Applications (2002)
- Volume: 22, Issue: 1, page 25-31
- ISSN: 1509-9415
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topKonrad Pióro. "On some finite groupoids with distributive subgroupoid lattices." Discussiones Mathematicae - General Algebra and Applications 22.1 (2002): 25-31. <http://eudml.org/doc/287718>.
@article{KonradPióro2002,
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).},
author = {Konrad Pióro},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {groupoid; subgroupoid lattice; distributive lattice; groupoids; subgroupoid lattices; distributive lattices; unions of subgroupoids},
language = {eng},
number = {1},
pages = {25-31},
title = {On some finite groupoids with distributive subgroupoid lattices},
url = {http://eudml.org/doc/287718},
volume = {22},
year = {2002},
}
TY - JOUR
AU - Konrad Pióro
TI - On some finite groupoids with distributive subgroupoid lattices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2002
VL - 22
IS - 1
SP - 25
EP - 31
AB - 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).
LA - eng
KW - groupoid; subgroupoid lattice; distributive lattice; groupoids; subgroupoid lattices; distributive lattices; unions of subgroupoids
UR - http://eudml.org/doc/287718
ER -
References
top- [1] G. Grätzer, General Lattice Theory, Akademie-Verlag, Berlin 1978. Zbl0436.06001
- [2] T. Evans and B. Ganter, Varieties with modular subalgebra lattices, Bull. Austr. Math. Soc. 28 (1983), 247-254. Zbl0545.08010
- [3] E.W. Kiss and M.A. Valeriote, Abelian algebras and the Hamiltonian property, J. Pure Appl. Algebra 87 (1993), 37-49. Zbl0779.08004
- [4] P.P. Pálfy, Modular subalgebra lattices, Algebra Universalis 27 (1990), 220-229. Zbl0708.08002
- [5] D. Sachs, The lattice of subalgebras of a Boolean algebra, Canad. J. Math. 14 (1962), 451-460. Zbl0105.25204
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