Erné, M.
(1993):
Distributive laws for concept lattices.
In: Algebra Universalis,
Vol. 30,
Verlag/Publisher: Birkhäuser Basel.
Erscheinungsjahr/Year: 1993.
Seiten/Pages: 538-580.
[Volltext] [Kurzfassung] [BibTeX]
[Endnote]
We study several kinds of distributivity for concept lattices of contexts. In particular, we find necessary and sufficient conditions for a concept lattice to be(1)distributive,(2)a frame (locale, complete Heyting algebra),(3)isomorphic to a topology,(4)completely distributive,(5)superalgebraic (i.e., algebraic and completely distributive).
@article{erne1993distributive,
author = {Erné, Marcel},
title = {Distributive laws for concept lattices},
journal = {Algebra Universalis},
publisher = {Birkhäuser Basel},
year = {1993},
volume = {30},
pages = {538-580},
url = {http://dx.doi.org/10.1007/BF01195382},
doi = {10.1007/BF01195382},
issn = {0002-5240},
keywords = {complete, concept, distributive, distributivity, fba, fca, lattice, math, theory},
abstract = {We study several kinds of distributivity for concept lattices of contexts. In particular, we find necessary and sufficient conditions for a concept lattice to be(1)distributive,(2)a frame (locale, complete Heyting algebra),(3)isomorphic to a topology,(4)completely distributive,(5)superalgebraic (i.e., algebraic and completely distributive).}
}
%0 = article
%A = Erné, Marcel
%D = 1993
%I = Birkhäuser Basel
%T = Distributive laws for concept lattices
%U = http://dx.doi.org/10.1007/BF01195382
Grätzer, G. & Lakser, H.
(1991):
On Complete Congruence Lattices of Complete Lattices.
In: Trans. Amer. Math. Soc.,
Ausgabe/Number: 1,
Vol. 327,
Erscheinungsjahr/Year: 1991.
Seiten/Pages: 385-405.
[BibTeX]
[Endnote]
@article{GratzerLasker,
author = {Grätzer, George and Lakser, Henry},
title = {On Complete Congruence Lattices of Complete Lattices},
journal = {Trans. Amer. Math. Soc.},
year = {1991},
volume = {327},
number = {1},
pages = {385--405},
keywords = {cited, complete, congruence, da, diplomarbeit, lattice}
}
%0 = article
%A = Grätzer, George and Lakser, Henry
%D = 1991
%T = On Complete Congruence Lattices of Complete Lattices
Hales, A. W.
(1964):
On the non-existence of free complete Boolean algebras.
In: Fundamentae Mathematica,
Vol. 54,
Erscheinungsjahr/Year: 1964.
Seiten/Pages: 45-66.
[Volltext] [BibTeX]
[Endnote]
@article{hales1964nonexistence,
author = {Hales, A. W.},
title = {On the non-existence of free complete Boolean algebras},
journal = {Fundamentae Mathematica},
year = {1964},
volume = {54},
pages = {45-66},
url = {http://matwbn.icm.edu.pl/tresc.php?wyd=1&tom=54},
keywords = {algebras, boolean, complete, existence, fca, free, lattice}
}
%0 = article
%A = Hales, A. W.
%D = 1964
%T = On the non-existence of free complete Boolean algebras
%U = http://matwbn.icm.edu.pl/tresc.php?wyd=1&tom=54