Publication details

Uniquely Complemented Posets

Authors

CHAJDA Ivan LÄNGER Helmut PASEKA Jan

Year of publication 2018
Type Article in Periodical
Magazine / Source ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007/s11083-017-9440-5
Doi http://dx.doi.org/10.1007/s11083-017-9440-5
Keywords Complemented poset; Uniquely complemented; Atomic; Atomistic; Distributive; LU-identity
Description 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.
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