Forcing extensions of partial lattices
| dc.creator | Wehrung, Friedrich | |
| dc.date | 2005-01-22 | |
| dc.date.accessioned | 2026-07-07T05:16:17Z | |
| dc.date.available | 2026-07-07T05:16:17Z | |
| dc.description | We prove the following result: Let K be a lattice, let D be a distributive lattice with zero, and let $ϕ$: Con K $\to$ D be a {∨, 0}-homomorphism, where Conc K denotes the {∨, 0}-semilattice of all finitely generated congruences of K. Then there are a lattice L, a lattice homomorphism f : K $\to$ L, and an isomorphism $\ga$: Conc L $\to$ D such that $\ga$ Conc f = $ϕ$. Furthermore, L and f satisfy many additional properties, for example: (i) L is relatively complemented. (ii) L has definable principal congruences. (iii) If the range of $ϕ$ is cofinal in D, then the convex sublattice of L generated by f[K] equals L. We mention the following corollaries, that extend many results obtained in the last decades in that area: -- Every lattice K such that Conc K is a lattice admits a congruence-preserving extension into a relatively complemented lattice. -- Every {∨, 0}-direct limit of a countable sequence of distributive lattices with zero is isomorphic to the semilattice of compact congruences of a relatively complemented lattice with zero. | |
| dc.identifier | https://arxiv.org/abs/math/0501378 | |
| dc.identifier | http://arxiv.org/abs/math/0501378 | |
| dc.identifier | Journal of Algebra 262, no. 1 (2003) 127--193 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73932 | |
| dc.subject | General Mathematics | |
| dc.subject | 06B10, 06B15, 06B25, 03C90 | |
| dc.title | Forcing extensions of partial lattices | |
| dc.type | text |