{"paper":{"title":"Detailed proof of a theorem on coincidence of homological dimensions of Fr\\'echet algebras of smooth functions on a manifold with the dimension of the manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.FA","authors_text":"Olga Ogneva","submitted_at":"2014-05-16T08:43:28Z","abstract_excerpt":"Given work contains the full text of the proof of the following assertion:\n  For the topological algebra $C^{\\infty}(\\mathcal{M})$ of smooth functions on a smooth $m$-dimensional real manifold $\\mathcal{M}$ the small global dimension $(\\mathop{\\mathrm{ds}} C^\\infty (\\mathcal{M}))$, the global homological dimension $(\\mathop{\\mathrm{dg}} C^\\infty (\\mathcal{M}))$ and the bidimension $(\\mathop{\\mathrm{db}} C^\\infty(\\mathcal{M}))$ are equal to $m$ (all dimensions are understood in the sense of the homology of topological (locally convex) algebras)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4094","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"}