Sublattices of lattices of order-convex sets, I. The main representation theorem
| dc.creator | Semenova, Marina V. | |
| dc.creator | Wehrung, Friedrich | |
| dc.date | 2005-01-21 | |
| dc.date.accessioned | 2026-07-07T05:16:14Z | |
| dc.date.available | 2026-07-07T05:16:14Z | |
| dc.description | For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some lattice of the form Co(P) iff L satisfies (S), (U), and (B). Furthermore, if L has an embedding into some Co(P), then it has such an embedding that preserves the existing bounds. If L is finite, then one can take P finite, of cardinality at most $2n^2-5n+4$, where n is the number of join-irreducible elements of L. On the other hand, the partially ordered set P can be chosen in such a way that there are no infinite bounded chains in P and the undirected graph of the predecessor relation of P is a tree. | |
| dc.identifier | https://arxiv.org/abs/math/0501341 | |
| dc.identifier | http://arxiv.org/abs/math/0501341 | |
| dc.identifier | Journal of Algebra 277, no. 2 (2004) 825--860 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73912 | |
| dc.subject | General Mathematics | |
| dc.subject | Primary: 06B05, 06B15, 06B23, 08C15. Secondary: 05B25, 05C05 | |
| dc.title | Sublattices of lattices of order-convex sets, I. The main representation theorem | |
| dc.type | text |