{"paper":{"title":"Monoids $\\mathrm{Mon}\\langle a,b:a^{\\alpha}b^{\\beta}a^{\\gamma}b^{\\delta}=b\\rangle$ admit finite complete rewriting systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alan Cain, Victor Maltcev","submitted_at":"2013-02-05T10:30:12Z","abstract_excerpt":"We prove that every monoid $\\mathrm{Mon}\\langle a,b:a^{\\alpha}b^{\\beta}a^{\\gamma}b^{\\delta}=b\\rangle$ admits a finite complete rewriting system. Furthermore we prove that $\\mathrm{Mon}\\langle a,b:ab^2a^2b^2=b\\rangle$ is non-hopfian, providing an example of a finitely presented non-residually finite monoid with linear Dehn function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0982","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"}