{"paper":{"title":"Congruence amalgamation of lattices","license":"","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Friedrich Wehrung (LMNO), George Gr\\\"atzer, Harry Lakser","submitted_at":"2005-01-22T11:36:02Z","abstract_excerpt":"J. Tuma proved an interesting \"congruence amalgamation\" result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: --A.P. Huhn proved that every distributive algebraic lattice $D$ with at most $\\aleph\\_1$ compact elements can be represented as the congruence lattice of a lattice $L$. We show that $L$ can be constructed as a locally finite relatively complemented lattice with zero. --We find a large class of lattices, the $\\omega$-congruence-finite lattices, that contains all locally finite countable lattices, in which every lattice has a r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501370","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"}