{"paper":{"title":"The word problem for some classes of Adian inverse semigroups -- II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Muhammad Inam","submitted_at":"2023-05-27T00:16:28Z","abstract_excerpt":"We introduce the notion of a subgraph generated by an $R$-word $r$ of the Sch\\\"{u}tzenberger graph of a positive word $w$, $S\\Gamma(w)$, where $w$ contains $r$ as its subword. We show that the word problem for a finitely presented Adian inverse semigroup $Inv\\langle X|R \\rangle$ is decidable if the subgraphs of $S\\Gamma(t)$, for all $t\\in X^+$, generated by all the $R$-words over the presentation $\\langle X|R\\rangle$, are finite. As a consequence of this result, we show that the word problem is decidable for some classes of one relation Adian inverse semigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.17312","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.17312/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}