Poset representations of distributive semilattices
| dc.creator | Wehrung, Friedrich | |
| dc.date | 2006-01-04 | |
| dc.date | 2007-11-23 | |
| dc.date.accessioned | 2026-07-07T09:45:41Z | |
| dc.date.available | 2026-07-07T09:45:41Z | |
| dc.description | We prove that for any distributive join-semilattice S, there are a meet-semilattice P with zero and a map f:PxP-->S such that f(x,z)<=f(x,y)vf(y,z) and x<=y implies that f(x,y)=0, for all x,y,z in P, together with the following conditions: (i) f(y,x)=0 implies that x=y, for all x<=y in P. (ii) For all x\leq y in P and all a,b in S, if f(y,x)=avb, then there are a positive integer n and a decomposition x=x_0<=x_1<=...<=x_n=y such that f(x_{i+1},x_i) lies either below a or below b, for all i < n. (iii) The subset {f(x,0)|x\in P} generates the semilattice S. Furthermore, any finite, bounded subset of P has a join, and P is bounded in case S is bounded. Furthermore, the construction is functorial on lattice-indexed diagrams of finite distributive (v,0,1)-semilattices. | |
| dc.description | To appear in Internat. J. Algebra Comput | |
| dc.identifier | https://arxiv.org/abs/math/0601058 | |
| dc.identifier | http://arxiv.org/abs/math/0601058 | |
| dc.identifier | International Journal of Algebra and Computation 18, 2 (2008) 321--356 | |
| dc.identifier | doi:10.1142/S0218196708004469 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163279 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Primary 06A06, 06A12. Secondary 06B10 | |
| dc.title | Poset representations of distributive semilattices | |
| dc.type | text |