{"paper":{"title":"Congruences on bicyclic extensions of a linearly ordered group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Du\\v{s}an Pagon, Kateryna Pavlyk, Oleg Gutik","submitted_at":"2011-11-10T06:37:44Z","abstract_excerpt":"In the paper we study inverse semigroups $\\mathscr{B}(G)$, $\\mathscr{B}^+(G)$, $\\bar{\\mathscr{B}}(G)$ and $\\bar{\\mathscr{B}}\\,^+(G)$ which are generated by partial monotone injective translations of a positive cone of a linearly ordered group $G$. We describe Green's relations on the semigroups $\\mathscr{B}(G)$, $\\mathscr{B}^+(G)$, $\\bar{\\mathscr{B}}(G)$ and $\\bar{\\mathscr{B}}\\,^+(G)$, their bands and show that they are simple, and moreover the semigroups $\\mathscr{B}(G)$ and $\\mathscr{B}^+(G)$ are bisimple. We show that for a commutative linearly ordered group $G$ all non-trivial congruences "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2401","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"}