Sublattices of lattices of order-convex sets, II. Posets of finite length
| 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 positive integer n, we denote by SUB (resp., SUBn) the class of all lattices that can be embedded into the lattice Co(P) of all order-convex subsets of a partially ordered set P (resp., P of length at most n). We prove the following results: (1) SUBn is a finitely based variety, for any n ≥ 1. (2) SUB2 is locally finite. (3) A finite atomistic lattice L without D-cycles belongs to SUB iff it belongs to SUB2; this result does not extend to the nonatomistic case. (4) SUBn is not locally finite for n ≥ 3. | |
| dc.identifier | https://arxiv.org/abs/math/0501340 | |
| dc.identifier | http://arxiv.org/abs/math/0501340 | |
| dc.identifier | International Journal of Algebra and Computation 13, no. 5 (2003) 543-564 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73911 | |
| dc.subject | General Mathematics | |
| dc.subject | Primary: 06B05, 06B15, 06B23, 08C15. Secondary: 05B25, 05C05 | |
| dc.title | Sublattices of lattices of order-convex sets, II. Posets of finite length | |
| dc.type | text |