Publication details
Uniquely Complemented Posets
| Authors | |
|---|---|
| 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 | |
| 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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