{"paper":{"title":"On the Anderson-Badawi $\\omega_{R[X]}(I[X])=\\omega_R(I)$ conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Peyman Nasehpour","submitted_at":"2014-01-02T15:56:41Z","abstract_excerpt":"Let $R$ be a commutative ring with an identity different from zero and $n$ be a positive integer. Anderson and Badawi, in their paper on $n$-absorbing ideals, define a proper ideal $I$ of a commutative ring $R$ to be an $n$-absorbing ideal of $R$, if whenever $x_1 \\cdots x_{n+1} \\in I$ for $x_1, \\ldots, x_{n+1} \\in R$, then there are $n$ of the $x_i$'s whose product is in $I$ and conjecture that $\\omega_{R[X]}(I[X])=\\omega_R(I)$ for any ideal $I$ of an arbitrary ring $R$, where $\\omega_R(I)= \\min \\{n\\colon\\text{$I$ is an $n$-absorbing ideal of $R$}\\}$. In the present paper, we use content form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0459","kind":"arxiv","version":4},"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"}