Representable posets and their order components

2007/05/29 by M. E. Adams, Michael E. Adams, Dominic van der Zypen +2
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras #math.LO #msc:06D50

paper · pdf · doi:10.48550/arxiv.0705.4259

06D50

arxiv created 2007/05/29 · arxiv updated 2009/12/01

Abstract

A partially ordered set P is representable if there is a bounded distributive lattice such that its ordered set of prime ideals is order-isomorphic to P. We show that if the order components of a poset P are representable, then so is P. Moreover, we provide an example disproving the converse.

Related

• Sub-representation of posets
• Stable representations of posets
• Structures of lattices which can be represented as the collection of all up-sets
• Algebraically equipped posets
• A simultaneous representation of a group and a bounded poset with lattice automorphisms and principal congruences