{"paper":{"title":"The stable and the real rank of Z-absorbing C*-algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Mikael Rordam","submitted_at":"2004-08-02T14:13:04Z","abstract_excerpt":"Suppose that A is a C*-algebra for which A is isomorphic to A tensor Z, where Z is the Jiang-Su algebra: a unital, simple, stably finite, separable, nuclear, infinite dimensional C*-algebra with the same Elliott invariant as the complex numbers. We show that:\n  (i) The Cuntz semigroup W(A) of equivalence classes of positive elements in matrix algebras over A is weakly unperforated.\n  (ii) If A is exact, then A is purely infinite if and only if A is traceless.\n  (iii) If A is separable and nuclear, then A is isomorphic to A tensor O_infty if and only if A is traceless.\n  (iv) If A is simple and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408020","kind":"arxiv","version":2},"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"}