{"paper":{"title":"Ring Of Real Analytic Functions on $[0,1]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.RA"],"primary_cat":"math.AC","authors_text":"Sagar Shrivastava, Vaibhav Pandey","submitted_at":"2016-11-11T11:51:42Z","abstract_excerpt":"We consider the ring of real analytic functions defined on $[0,1]$, i.e. $$C^{\\omega}[0,1] =\\lbrace f :[0,1] \\longrightarrow \\mathbb{R} | f \\text{ is analytic on } [0,1]\\rbrace$$ In this article, we explore the nature of ideals in this ring. It is well known that the ring $C[0,1]$ of real valued continuous functions on $[0,1]$ has precisely the following maximal ideals: $$\\text{For } \\gamma \\in [0,1], M_{\\gamma} := \\lbrace f \\in C[0,1] | f(\\gamma) =0\\rbrace$$ It has been proved that each such $M_{\\gamma}$ is infinitely generated, in-fact uncountably generated. Observe that $C^{\\omega}[0,1]$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03667","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"}