# 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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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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