{"paper":{"title":"On \\phi-n-absorbing primary ideals of commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ahmad Yousefian Darani, Hojjat Mostafanasab","submitted_at":"2015-02-28T09:55:36Z","abstract_excerpt":"All rings are commutative with $1$ and $n$ is a positive integer. Let $\\phi: J(R)\\to J(R)\\cup{\\emptyset}$ be a function where $J(R)$ denotes the set of all ideals of $R$. We say that a proper ideal $I$ of $R$ is $\\phi$-$n$-absorbing primary if whenever $a_1,a_2,...,a_{n+1}\\in R$ and $a_1a_2\\cdots a_{n+1}\\in I\\backslash\\phi(I)$, either $a_1a_2\\cdots a_n\\in I$ or the product of $a_{n+1}$ with $(n-1)$ of $a_1,...,a_n$ is in $\\sqrt{I}$. The aim of this paper is to investigate the concept of $\\phi$-$n$-absorbing primary ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00108","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"}