Uniquely complemented posets (Q1789052)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Uniquely complemented posets |
scientific article; zbMATH DE number 6949473
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniquely complemented posets |
scientific article; zbMATH DE number 6949473 |
Statements
Uniquely complemented posets (English)
0 references
9 October 2018
0 references
It is known that every complemented distributive poset is uniquely complemented, and that the converse statement (that uniquely complemented posets are distributive) fails even for lattices. This paper provides conditions that force a uniquely complemented poset to be distributive. In particular, the paper provides proofs that uniquely complemented posets are distributive in the following situations: (i) the poset is atomistic, (ii) the completely join-irreducible elements of the poset are atoms and the poset satisfies the descending chain condition, or (iii) the poset is modular and satisfies the descending chain condition.
0 references
complemented poset
0 references
uniquely complemented
0 references
atomic
0 references
atomistic
0 references
distributive
0 references
LU-identity
0 references
