{"paper":{"title":"Integrality over ideal semifiltrations","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Darij Grinberg","submitted_at":"2019-07-13T20:35:30Z","abstract_excerpt":"We study integrality over rings (all commutative in this paper) and over ideal semifiltrations (a generalization of integrality over ideals). We begin by reproving classical results, such as a version of the \"faithful module\" criterion for integrality over a ring, the transitivity of integrality, and the theorem that sums and products of integral elements are again integral. Then, we define the notion of integrality over an ideal semifiltration (a sequence $\\left( I_0,I_1,I_2,\\ldots\\right)$ of ideals satisfying $I_0 =A$ and $I_a I_b \\subseteq I_{a+b}$ for all $a,b\\in\\mathbb{N}$), which general"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06125","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"}