A characterization of well-founded algebraic lattices
| dc.creator | Chakir, Ilham | |
| dc.creator | Pouzet, Maurice | |
| dc.date | 2008-12-12 | |
| dc.date.accessioned | 2026-07-07T12:12:22Z | |
| dc.date.available | 2026-07-07T12:12:22Z | |
| dc.description | We characterize well-founded algebraic lattices by means of forbidden subsemilattices of the join-semilattice made of their compact elements. More specifically, we show that an algebraic lattice $L$ is well-founded if and only if $K(L)$, the join-semilattice of compact elements of $L$, is well-founded and contains neither $[ω]^{<ω}$, nor $\underlineΩ(ω^*)$ as a join-subsemilattice. As an immediate corollary, we get that an algebraic modular lattice $L$ is well-founded if and only if $K(L)$ is well-founded and contains no infinite independent set. If $K(L)$ is a join-subsemilattice of $I_{<ω}(Q)$, the set of finitely generated initial segments of a well-founded poset $Q$, then $L$ is well-founded if and only if $K(L)$ is well-quasi-ordered. | |
| dc.description | 19 pages, 2 pictures, submitted | |
| dc.identifier | https://arxiv.org/abs/0812.2300 | |
| dc.identifier | http://arxiv.org/abs/0812.2300 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210526 | |
| dc.subject | Combinatorics | |
| dc.subject | Logic | |
| dc.subject | 06A12, 06B35 | |
| dc.title | A characterization of well-founded algebraic lattices | |
| dc.type | text |