{"paper":{"title":"Flat semilattices","license":"","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Friedrich Wehrung (LMNO), George Gr\\\"atzer","submitted_at":"2005-01-25T08:24:15Z","abstract_excerpt":"Let $A$, $B$, and $S$ be (v,0)-semilattices and let $f: A\\to B$ be a (v,0)-embedding. Then the canonical map, $f \\otimes \\id\\_S$, of the tensor product $A \\otimes S$ into the tensor product $B \\otimes S$ is not necessarily an embedding. The (v,0)-semilattice $S$ is flat, if for every embedding $f : A\\to B$, the canonical map $f\\otimes\\id$ is an embedding. We prove that a (v,0)-semilattice $S$ is flat if and only if it is distributive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501431","kind":"arxiv","version":1},"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"}