{"paper":{"title":"On a problem of M. Kambites regarding abundant 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":"2010-06-18T12:36:49Z","abstract_excerpt":"A semigroup is \\emph{regular} if it contains at least one idempotent in each $\\mathcal{R}$-class and in each $\\mathcal{L}$-class. A regular semigroup is \\emph{inverse} if satisfies either of the following equivalent conditions: (i) there is a unique idempotent in each $\\mathcal{R}$-class and in each $\\mathcal{L}$-class, or (ii) the idempotents commute.\n  Analogously, a semigroup is \\emph{abundant} if it contains at least one idempotent in each $\\mathcal{R}^*$-class and in each $\\mathcal{L}^*$-class. An abundant semigroup is \\emph{adequate} if its idempotents commute. In adequate semigroups, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3677","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"}