{"paper":{"title":"The Brian\\c{c}on-Skoda Theorem and Coefficient Ideals for Non m-Primary Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Aline Hosry, Ian M. Aberbach","submitted_at":"2010-10-06T04:48:13Z","abstract_excerpt":"We generalize a Brian\\c{c}on-Skoda type theorem first studied by Aberbach and Huneke. With some conditions on a regular local ring $(R,\\m)$ containing a field, and an ideal $I$ of $R$ with analytic spread $\\ell$ and a minimal reduction $J$, we prove that for all $w \\geq -1$, $ \\bar{I^{\\ell+w}} \\subseteq J^{w+1} \\mathfrak{a} (I,J),$ where $\\mathfrak{a}(I,J)$ is the coefficient ideal of $I$ relative to $J$, i.e. the largest ideal $\\mathfrak{b}$ such that $I\\mathfrak{b}=J\\mathfrak{b}$. Previously, this result was known only for $\\m$-primary ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1061","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"}