{"paper":{"title":"The minimal ideal in multiplier algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"P. W. Ng, Shuang Zhang, Victor Kaftal","submitted_at":"2017-05-11T19:31:57Z","abstract_excerpt":"Let $\\mathcal A$ be a simple, $\\sigma$-unital, non-unital, non-elementary C*-algebra and let $I_{min}$ be the intersection of all the ideals of $\\mathcal M(\\mathcal A)$ that properly contain $\\mathcal A$. $I_{min}$ coincides with the ideal defined by Lin (Simple C*-algebras with continuous scales and simple corona algebras. 112, (1991) Proc. Amer.Math. Soc) in terms of approximate units of $\\mathcal A$ and $I_{min}/\\mathcal A$ is purely infinite and simple. If $\\mathcal A$ is separable, or if $\\mathcal A$ has the (SP) property and its dimension semigroup $D(\\mathcal A)$ of Murray-von Neumann e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04362","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"}