{"paper":{"title":"Homomorphisms and principal congruences of bounded lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"George Gr\\\"atzer","submitted_at":"2015-07-12T20:32:02Z","abstract_excerpt":"Two years ago, I characterized the order $\\Princl L$ of principal congruences of a bounded lattice $L$ as a bounded order.\n  If $K$ and $L$ are bounded lattices and $\\gf$ is a \\zo homomorphism of $K$ into~$L$, then there is a natural isotone \\zo-map $\\gf_{\\Hom}$ from $\\Princl K$ into $\\Princl L$.\n  We prove the converse: For bounded orders $P$ and $Q$ and an isotone \\zo map $\\gy$ of $P$ into $Q$, we represent $P$ and $Q$ as $\\Princl K$ and $\\Princl L$ for bounded lattices $K$ and $L$ with a \\zo homomorphism $\\gf$ of $K$ into $L$, so that $\\gy$ is represented as $\\gf_{\\Hom}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03270","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"}