{"paper":{"title":"On the Krull Intersection Theorem in Function Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.FA"],"primary_cat":"math.CV","authors_text":"Amol Sasane, Raymond Mortini, Rudolf Rupp","submitted_at":"2016-05-26T09:28:24Z","abstract_excerpt":"A version of the Krull Intersection Theorem states that for Noetherian domains, the Krull intersection $ki(I)$ of every proper ideal $I$ is trivial; that is $$ ki(I):=\\displaystyle\\bigcap_{n=1}^\\infty I^n = \\{0\\}. $$ We investigate the validity of this result for various function algebras $R$, present ideals $I$ of $R$ for which $ ki(I)\\neq \\{0\\}$, and give conditions on $I$ so that $ki(I)=\\{0\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08204","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"}