{"paper":{"title":"Lee monoids are non-finitely based while the sets of their isoterms are finitely based","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Olga Sapir","submitted_at":"2016-10-30T22:32:16Z","abstract_excerpt":"We establish a new sufficient condition under which a monoid is non-finitely based and apply this condition to 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 $\\ell$).\n  We show that every monoid which generates a variety containing $L_5^1$ and is contained in the variety generated by $L_\\ell^1$ for some $\\ell \\ge 5$ is non-finitely based. We establish this result by analyzing $\\tau$-terms for $M$ where $\\tau$ is certain non-trivial congruence on the free semigroup, tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09721","kind":"arxiv","version":6},"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"}