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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0311461","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2003-11-26T04:43:57Z","cross_cats_sorted":[],"title_canon_sha256":"19a37e466b02c32ef548ef231ce70374ac5514fbfed95c8c3f2f0c3911c9e840","abstract_canon_sha256":"3928d4bc8b9f7790d6fcfdd2122e41e67d9fc6d24516f112a4330ad580e8a1de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.713612Z","signature_b64":"qjeOqmfExfBSYqVSlHptKSdsQyXrWwYr3TccS0ZTBjBRsB/a2iw+oLRVEWfG4elfzf6Iw5S9QVT+KfwiwL1rAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7efb3449db8273b522e914b0bf35206a255db8b48782526a60aa79c7f7a072d1","last_reissued_at":"2026-05-18T01:05:26.713116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.713116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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