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We establish this result by analyzing $\\tau$-terms for $M$ where $\\tau$ is certain non-trivial congruence on the free semigroup, tha"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.09721","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-30T22:32:16Z","cross_cats_sorted":[],"title_canon_sha256":"54c1002c3d596b01314272d1094b94e8605a315a5de9d7d745006a04edf66d77","abstract_canon_sha256":"90088a4cef74052c9fa37ecb1f895bb8edf9d69cf6644761fdddaa7e9a279ee9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:45.210593Z","signature_b64":"kwiVwkyo9dNj+80QjMrfLfZL4POgct6uPCZuec/qkCh7r8RbVllJnCaS+RFL8GX9sieDDvaUqHiiVJfRnwTQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3da0b91083bd35782335416d6771d1123b6e38f4fb0f5056fdb761bcadd8c386","last_reissued_at":"2026-05-18T00:24:45.209958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:45.209958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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