{"paper":{"title":"On certain semigroups of partial contractions of a finite chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. Umar, M. M. Zubairu","submitted_at":"2018-03-07T11:33:45Z","abstract_excerpt":"Let $[n]=\\{1,2,\\ldots,n\\}$ be a finite chain and let $\\mathcal{P}_{n}$ be the semigroup of partial transformations on $[n]$. Let $\\mathcal{CP}_{n}=\\{\\alpha\\in \\mathcal{P}_{n}: (for ~all~x,y\\in Dom~\\alpha)~|x\\alpha-y\\alpha|\\leq|x-y|\\}$ be the subsemigroup of partial contraction mappings on $[n]$. We have shown that the semigroup $\\mathcal{CP}_{n}$ and some of its subsemigroups are nonregular left abundant semigroups for all $n$ but not right abundant for $n\\geq 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02604","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"}