{"paper":{"title":"Big tight closure test elements for some non-reduced excellent rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Rodney Y. Sharp","submitted_at":"2011-08-08T09:52:32Z","abstract_excerpt":"This paper is concerned with existence of big tight closure test elements for a commutative Noetherian ring $R$ of prime characteristic $p$. Let $R^{\\circ}$ denote the complement in $R$ of the union of the minimal prime ideals of $R$. A big test element for $R$ is an element of $R^{\\circ}$ which can be used in every tight closure membership test for every $R$-module, and not just the finitely generated ones. The main results of the paper are that, if $R$ is excellent and satisfies condition $(R_0)$, and $c \\in R^{\\circ}$ is such that $R_c$ is Gorenstein and weakly $F$-regular, then some power "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1660","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"}