{"paper":{"title":"Lee monoid $L_4^1$ is non-finitely based","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Inna Mikhailova, Olga Sapir","submitted_at":"2017-10-01T17:29:40Z","abstract_excerpt":"We establish a new sufficient condition under which a monoid is non-finitely based and apply this condition to show that the 9-element monoid $L_4^1$ is non-finitely based. The monoid $L_4^1$ was the only unsolved case in the finite basis problem for Lee monoids $L_\\ell^1$, obtained by adjoining an identity element to the semigroup generated by two idempotents $a$ and $b$ subjected to the relation $0=abab \\cdots$ (length $\\ell$). We also prove a syntactic sufficient condition which is equivalent to the sufficient condition of Lee under which a semigroup is non-finitely based. This gives a new "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00820","kind":"arxiv","version":5},"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"}