{"paper":{"title":"On monoids 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":["math.GN"],"primary_cat":"math.GR","authors_text":"Inna Pozdnyakova, Oleg Gutik","submitted_at":"2013-11-24T21:49:07Z","abstract_excerpt":"We study 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 order. We show that $\\mathscr{I\\!O}\\!_{\\infty}(\\mathbb{Z}^n_{\\operatorname{lex}})$ is bisimple and establish its projective congruences. We prove that $\\mathscr{I\\!O}\\!_{\\infty}(\\mathbb{Z}^n_{\\operatorname{lex}})$ is finitely generated, and for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6175","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"}