{"paper":{"title":"A new lattice construction: the box product","license":"","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Friedrich Wehrung (LMNO), George Gr\\\"atzer","submitted_at":"2005-01-24T17:04:10Z","abstract_excerpt":"In a recent paper, the authors have proved that for lattices A and B with zero, the isomorphism $Conc(A \\otimes B)\\cong Conc A \\otimes Conc B$, holds, provided that the tensor product satisfies a very natural condition (of being capped) implying that $A\\otimes B$ is a lattice. In general, $A \\otimes B$ is not a lattice; for instance, we proved that $M\\_3\\otimes F(3)$ is not a lattice. In this paper, we introduce a new lattice construction, the box product for arbitrary lattices. The tensor product construction for complete lattices introduced by G. N. Raney in 1960 and by R. Wille in 198"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501418","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"}