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Uniquely Complemented Posets

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CHAJDA Ivan LÄNGER Helmut PASEKA Jan

Rok publikování 2018
Druh Článek v odborném periodiku
Časopis / Zdroj ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://link.springer.com/article/10.1007/s11083-017-9440-5
Doi http://dx.doi.org/10.1007/s11083-017-9440-5
Klíčová slova Complemented poset; Uniquely complemented; Atomic; Atomistic; Distributive; LU-identity
Popis 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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