| CHAJDA, Ivan, Helmut LÄNGER and Jan PASEKA. Uniquely Complemented Posets. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS. DORDRECHT: SPRINGER, 2018, vol. 35, No 3, p. 421-431. ISSN 0167-8094. Available from: https://dx.doi.org/10.1007/s11083-017-9440-5. |
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@article{1482813,
author = {Chajda, Ivan and Länger, Helmut and Paseka, Jan},
article_location = {DORDRECHT},
article_number = {3},
doi = {http://dx.doi.org/10.1007/s11083-017-9440-5},
keywords = {Complemented poset; Uniquely complemented; Atomic; Atomistic; Distributive; LU-identity},
language = {eng},
issn = {0167-8094},
journal = {ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS},
title = {Uniquely Complemented Posets},
url = {https://link.springer.com/article/10.1007/s11083-017-9440-5},
volume = {35},
year = {2018}
}
TY - JOUR
ID - 1482813
AU - Chajda, Ivan - Länger, Helmut - Paseka, Jan
PY - 2018
TI - Uniquely Complemented Posets
JF - ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
VL - 35
IS - 3
SP - 421-431
EP - 421-431
PB - SPRINGER
SN - 01678094
KW - Complemented poset
KW - Uniquely complemented
KW - Atomic
KW - Atomistic
KW - Distributive
KW - LU-identity
UR - https://link.springer.com/article/10.1007/s11083-017-9440-5
L2 - https://link.springer.com/article/10.1007/s11083-017-9440-5
N2 - We study complementation in bounded posets. It is known and easy to see that every complemented distributive poset is uniquely complemented. The converse statement is not valid, even for lattices. In the present paper we provide conditions that force a uniquely complemented poset to be distributive. For atomistic resp. atomic posets as well as for posets satisfying the descending chain condition we find sufficient conditions in the form of so-called LU-identities. It turns out that for finite posets these conditions are necessary and sufficient.
ER -
CHAJDA, Ivan, Helmut LÄNGER and Jan PASEKA. Uniquely Complemented Posets. \textit{ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS}. DORDRECHT: SPRINGER, 2018, vol.~35, No~3, p.~421-431. ISSN~0167-8094. Available from: https://dx.doi.org/10.1007/s11083-017-9440-5.
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