{"paper":{"title":"Topological stable rank of inclusions of unital C*-algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hiroyuki Osaka, Tamotsu Teruya","submitted_at":"2003-11-26T04:43:57Z","abstract_excerpt":"Let $1 \\in A \\subset B$ be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of $B$ ($= \\tsr(B)$) when $A$ has topological stable rank one. We show that $\\tsr(B) \\leq 2$ when $A$ is a tsr boundedly divisible algebra, in particular, $A$ is a C*-minimal tensor product $UHF \\otimes\n D$ with $\\tsr(D) = 1$. When $G$ is a finite group and $\\alpha$ is an action of $G$ on UHF, we know that a crossed product algebra $UHF \\rtimes_\\alpha G$ has topological stable rank less than or equal to two.\n  These results are affirmative datum to a generaliza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311461","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"}