{"paper":{"title":"An elegant 3-basis for inverse semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Joao Araujo, Michael Kinyon","submitted_at":"2010-03-21T21:01:20Z","abstract_excerpt":"It is well known that in every inverse semigroup the binary operation and the unary operation of inversion satisfy the following three identities: [\\quad x=(xx')x \\qquad \\quad (xx')(y'y)=(y'y)(xx') \\qquad \\quad (xy)z=x(yz\"). ] The goal of this note is to prove the converse, that is, we prove that an algebra of type $<2,1>$ satisfying these three identities is an inverse semigroup and the unary operation coincides with the usual inversion on such semigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4028","kind":"arxiv","version":3},"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"}