{"paper":{"title":"A note on the quintasymptotic prime ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Reza Naghipour, Saeed Jahandoust","submitted_at":"2013-08-29T12:31:01Z","abstract_excerpt":"Let $R$ denote a commutative Noetherian ring, $I$ an ideal of $R$, and let $S$ be a multiplicatively closed subset of $R$. In \\cite{Ra1}, Ratliff showed that the sequence of sets ${\\rm Ass}_RR/\\bar{I}\\subseteq {\\rm Ass}_RR/\\bar{I^2} \\subseteq {\\rm Ass}_R R/\\bar{I^3}\\subseteq \\dots $ increases and eventually stabilizes to a set denoted $\\bar{A^\\ast}(I)$. In \\cite{Mc2}, S. McAdam gave an interesting description of $\\bar{A^\\ast}(I)$ by making use of $R[It,t^{-1}]$, the Rees ring of $I$. In this paper, we give a second description of $\\bar{A^\\ast}(I)$ by making use of the Rees valuation rings of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6449","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"}