{"paper":{"title":"Reducibility versus definability for pseudovarieties of semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"J. Almeida, O. Kl\\'ima","submitted_at":"2016-06-13T18:23:12Z","abstract_excerpt":"It is easy to show that a pseudovariety which is reducible with respect to an implicit signature $\\sigma$ for the equation $x=y$ can also be defined by $\\sigma$-identities. We present several negative examples for the converse using signatures in which the pseudovarieties are usually defined. An ordered example issue from the extended Straubing-Th\\'erien hierarchy of regular languages is also shown to provide a positive example for the inequality $x\\le y$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04059","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"}