{"paper":{"title":"A Less Restrictive Brian\\c{c}on-Skoda Theorem with Coefficients","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":"2010-10-06T04:49:44Z","abstract_excerpt":"The Brian\\c{c}on-Skoda theorem in its many versions has been studied by algebraists for several decades. In this paper, under some assumptions on an F-rational local ring $(R,\\m)$, and an ideal $I$ of $R$ of analytic spread $\\ell$ and height $g < \\ell$, we improve on two theorems by Aberbach and Huneke. Let $J$ be a reduction of $I$. We first give results on when the integral closure of $I^\\ell$ is contained in the product $J I_{\\ell-1}$, where $I_{\\ell-1}$ is the intersection of the primary components of $I$ of height $\\leq \\ell-1$. In the case that $R$ is also Gorenstein, we give results on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1062","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"}