{"paper":{"title":"Quintasymptotic sequences over an ideal and quintasymptotic cograde","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Reza Naghipour, Saeed Jahandoust","submitted_at":"2013-08-28T03:38:42Z","abstract_excerpt":"Let $I$ denote an ideal of a Noetherian ring $R$. The purpose of this article is to introduce the concepts of quintasymptotic sequences over $I$ and quintasymptotic cograde of $I$, and it is shown that they play a role analogous to quintessential sequences over $I$ and quintessential cograde of $I$, given in \\cite{Ra1}. Also, we show that, if $R$ is local, then the quintasymptotic cograde of $I$ is unambiguously defined and behaves well when passing to certain related local rings. Finally, we use this cograde to characterize of two classes of local rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6048","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"}