{"paper":{"title":"Generators for the $C^m$-closures of Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG","math.RA"],"primary_cat":"math.CA","authors_text":"Charles Fefferman, Garving K. Luli","submitted_at":"2019-02-11T01:04:25Z","abstract_excerpt":"Let $\\mathscr{R}$ denote the ring of real polynomials on $\\mathbb{R}^{n}$. Fix $m\\geq 0$, and let $A_{1},\\cdots ,A_{M}\\in \\mathscr{R}$. The $ C^{m}$-closure of $\\left( A_{1},\\cdots ,A_{M}\\right) $, denoted here by $ \\left[ A_{1},\\cdots ,A_{M};C^{m}\\right] $, is the ideal of all $f\\in \\mathscr{R}$ expressible in the form $f=F_{1}A_{1}+\\cdots +F_{M}A_{M}$ with each $F_{i}\\in C^{m}\\left( \\mathbb{R}^{n}\\right) $.\n  In this paper we exhibit an algorithm to compute generators for $\\left[ A_{1},\\cdots ,A_{M};C^{m}\\right] $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03692","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"}