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).
Description
SpringerLink - Algebra Universalis, Volume 30, Number 4
%0 Journal Article
%1 erne1993distributive
%A Erné, Marcel
%D 1993
%I Birkhäuser Basel
%J Algebra Universalis
%K complete concept distributive distributivity fba fca lattice math theory
%P 538-580
%R 10.1007/BF01195382
%T Distributive laws for concept lattices
%U http://dx.doi.org/10.1007/BF01195382
%V 30
%X 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,
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).},
added-at = {2010-12-19T13:14:14.000+0100},
affiliation = {Institut für Mathematik Universität Hannover Hannover Germany},
author = {Erné, Marcel},
biburl = {https://www.bibsonomy.org/bibtex/2dd7f97b10532feab21d486ebb6783939/sdo},
description = {SpringerLink - Algebra Universalis, Volume 30, Number 4},
doi = {10.1007/BF01195382},
interhash = {f30c769c54f5eb98962742b324651451},
intrahash = {dd7f97b10532feab21d486ebb6783939},
issn = {0002-5240},
issue = {4},
journal = {Algebra Universalis},
keyword = {Mathematics and Statistics},
keywords = {complete concept distributive distributivity fba fca lattice math theory},
pages = {538-580},
publisher = {Birkhäuser Basel},
timestamp = {2010-12-19T13:14:15.000+0100},
title = {Distributive laws for concept lattices},
url = {http://dx.doi.org/10.1007/BF01195382},
volume = 30,
year = 1993
}