{"paper":{"title":"The semigroup of partial co-finite isometries of positive integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Anatolii Savchuk, Oleg Gutik","submitted_at":"2019-04-14T06:46:34Z","abstract_excerpt":"The semigroup $\\mathbf{I}\\mathbb{N}_{\\infty}$ of all partial co-finite isometries of positive integers is studied. We describe Green's relations on the semigroup $\\mathbf{I}\\mathbb{N}_{\\infty}$, its band and proved that $\\mathbf{I}\\mathbb{N}_{\\infty}$ is a simple $E$-unitary $F$-inverse semigroup. We described the least group congruence $\\mathfrak{C}_{\\mathbf{mg}}$ on $\\mathbf{I}\\mathbb{N}_{\\infty}$ and proved that the quotient-semigroup $\\mathbf{I}\\mathbb{N}_{\\infty}/\\mathfrak{C}_{\\mathbf{mg}}$ is isomorphic to the additive group of integers. An example of a non-group congruence on the semigr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06638","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"}