{"paper":{"title":"On $\\kappa$-reducibility of pseudovarieties of the form $\\bf V*\\bf D$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Concei\\c{c}\\~ao Nogueira, Jos\\'e Carlos Costa, M. Lurdes Teixeira","submitted_at":"2016-02-09T15:09:32Z","abstract_excerpt":"This paper deals with the reducibility property of semidirect products of the form $\\bf V*\\bf D$ relatively to graph equation systems, where $\\bf D$ denotes the pseudovariety of definite semigroups. We show that, if the pseudovariety $\\bf V$ is reducible with respect to the canonical signature $\\kappa$ consisting of the multiplication and the $(\\omega-1)$-power, then $\\bf V*\\bf D$ is also reducible with respect to $\\kappa$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03020","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"}