{"paper":{"title":"On the closure of the extended bicyclic semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Iryna Fihel, Oleg Gutik","submitted_at":"2011-12-30T09:36:02Z","abstract_excerpt":"In the paper we study the semigroup $\\mathscr{C}_{\\mathbb{Z}}$ which is a generalization of the bicyclic semigroup. We describe main algebraic properties of the semigroup $\\mathscr{C}_{\\mathbb{Z}}$ and prove that every non-trivial congruence $\\mathfrak{C}$ on the semigroup $\\mathscr{C}_{\\mathbb{Z}}$ is a group congruence, and moreover the quotient semigroup $\\mathscr{C}_{\\mathbb{Z}}/\\mathfrak{C}$ is isomorphic to a cyclic group. Also we show that the semigroup $\\mathscr{C}_{\\mathbb{Z}}$ as a Hausdorff semitopological semigroup admits only the discrete topology. Next we study the closure $\\oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0090","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"}