{"paper":{"title":"On monoids of injective partial cofinite selfmaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Du\\v{s}an Repov\\v{s}, Oleg Gutik","submitted_at":"2015-12-11T20:02:43Z","abstract_excerpt":"We study the semigroup $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ of injective partial cofinite selfmaps of an infinite cardinal $\\lambda$. We show that $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is a bisimple inverse semigroup and each chain of idempotents in $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is contained in a bicyclic subsemigroup of $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$, we describe the Green relations on $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ and we prove that every non-trivial congruence on $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is a group congruence. Also, we describe the structure of the quotient semigroup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03779","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"}