Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice
Discussiones Mathematicae - General Algebra and Applications (2008)
- Volume: 28, Issue: 2, page 251-259
- ISSN: 1509-9415
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Abstract
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topIvan Chajda, and Helmut Länger. "Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice." Discussiones Mathematicae - General Algebra and Applications 28.2 (2008): 251-259. <http://eudml.org/doc/276839>.
@article{IvanChajda2008,
abstract = {Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.},
author = {Ivan Chajda, Helmut Länger},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {bounded lattice; antitone involution; complemented element},
language = {eng},
number = {2},
pages = {251-259},
title = {Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice},
url = {http://eudml.org/doc/276839},
volume = {28},
year = {2008},
}
TY - JOUR
AU - Ivan Chajda
AU - Helmut Länger
TI - Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 2
SP - 251
EP - 259
AB - Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.
LA - eng
KW - bounded lattice; antitone involution; complemented element
UR - http://eudml.org/doc/276839
ER -
References
top- [1] G. Birkhoff, Lattice Theory, AMS, Providence, R. I., 1979.
- [2] I. Chajda and H. Länger, Bounded lattices with antitone involution the complemented elements of which form a sublattice, J. Algebra Discrete Structures 6 (2008), 13-22. Zbl1159.06005
- [3] G. Grätzer, General Lattice Theory, Birkhäuser, Basel 1998. Zbl0909.06002
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