{"paper":{"title":"Ideals in Rings and Intermediate Rings of Measurable Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.GN"],"primary_cat":"math.FA","authors_text":"Joshua Sack, Sagarmoy Bag, Sudip Kumar Acharyya","submitted_at":"2018-06-07T18:57:06Z","abstract_excerpt":"The set of all maximal ideals of the ring $\\mathcal{M}(X,\\mathcal{A})$ of real valued measurable functions on a measurable space $(X,\\mathcal{A})$ equipped with the hull-kernel topology is shown to be homeomorphic to the set $\\hat{X}$ of all ultrafilters of measurable sets on $X$ with the Stone-topology. This yields a complete description of the maximal ideals of $\\mathcal{M}(X,\\mathcal{A})$ in terms of the points of $\\hat{X}$. It is further shown that the structure spaces of all the intermediate subrings of $\\mathcal{M}(X,\\mathcal{A})$ containing the bounded measurable functions are one and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02860","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"}