{"paper":{"title":"The Bass and topological stable ranks for algebras of almost periodic functions on the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Raymond Mortini, Rudolf Rupp","submitted_at":"2014-02-19T21:05:40Z","abstract_excerpt":"Let $\\Lambda$ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras ${\\rm AP}_\\Lambda=\\{f\\in {\\rm AP}: \\sigma(f)\\subseteq \\Lambda\\}$ of almost periodic functions on the real line and with Bohr spectrum in $\\Lambda$ are infinite whenever the algebraic dimension of the $\\mathbb Q$-vector space generated by $\\Lambda$ is infinite. This extends Su\\'arez's result for ${\\rm AP}_\\mathbb R={\\rm AP}$. Also considered are general subalgebras of AP."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4825","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"}