{"paper":{"title":"Congruences on the monoid of monotone injective partial selfmaps of $L_n\\times_{\\operatorname{lex}}\\mathbb{Z}$ with co-finite domains and images","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Inna Pozdniakova, Oleg Gutik","submitted_at":"2014-07-25T13:43:21Z","abstract_excerpt":"We study congruences of the semigroup $\\mathscr{I\\!O}\\!_{\\infty}(\\mathbb{Z}^n_{\\operatorname{lex}})$ of monotone injective partial selfmaps of the set of $L_n\\times_{\\operatorname{lex}}\\mathbb{Z}$ having co-finite domain and image, where $L_n\\times_{\\operatorname{lex}}\\mathbb{Z}$ is the lexicographic product of $n$-elements chain and the set of integers with the usual linear order. The structure of the sublattice of congruences on $\\mathscr{I\\!O}\\!_{\\infty}(\\mathbb{Z}^n_{\\operatorname{lex}})$ which contain in the least group congruence is described."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6892","kind":"arxiv","version":3},"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"}