{"paper":{"title":"Cevian operations on distributive lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Friedrich Wehrung (LMNO)","submitted_at":"2019-01-22T10:55:39Z","abstract_excerpt":"We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x $\\in$ D | a $\\le$ b $\\lor$ x} has a countable coinitial subset, such that D does not carry any binary operation - satisfying the identities x $\\le$ y $\\lor$(x-y),(x-y)$\\land$(y-x) = 0, and x-z $\\le$ (x-y)$\\lor$(y-z). In particular, D is not a homomorphic image of the lattice of all finitely generated convex {\\ell}-subgroups of any (not necessarily Abelian) {\\ell}-group. It has $\\aleph 2 elements. This solves negatively a few problems stated by Iberkleid, Mart{\\'i}nez, and McGo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07548","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}