{"paper":{"title":"$E$-solid locally inverse semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Istv\\'an Szittyai, M\\'aria B. Szendrei, Tam\\'as D\\'ek\\'any","submitted_at":"2018-07-03T16:25:54Z","abstract_excerpt":"We prove that if $S$ is an $E$-solid locally inverse semigroup, and $\\rho$ is an inverse semigroup congruence on $S$ such that the idempotent classes of $\\rho$ are completely simple semigroups then $S$ is embeddable into a $\\lambda$-semidirect product of a completely simple semigroup by $S/\\rho$. Consequently, the $E$-solid locally inverse semigroups turn out to be, up to isomorphism, the regular subsemigroups of $\\lambda$-semidirect products of completely simple semigroups by inverse semigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01265","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"}