{"paper":{"title":"On a semitopological polycyclic monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Oleg Gutik, Serhii Bardyla","submitted_at":"2016-01-06T12:08:24Z","abstract_excerpt":"We study algebraic structure of the $\\lambda$-polycyclic monoid $P_{\\lambda}$ and its topologizations. We show that the $\\lambda$-polycyclic monoid for an infinite cardinal $\\lambda\\geqslant 2$ has similar algebraic properties so has the polycyclic monoid $P_n$ with finitely many $n\\geqslant 2$ generators. In particular we prove that for every infinite cardinal $\\lambda$ the polycyclic monoid $P_{\\lambda}$ is a congruence-free combinatorial $0$-bisimple $0$-$E$-unitary inverse semigroup. Also we show that every non-zero element $x$ is an isolated point in $(P_{\\lambda},\\tau)$ for every Hausdor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01151","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"}