Uniquely Complemented Posets

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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.
Related projects:	Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti