{"paper":{"title":"Symmetric polynomials and non-finitely generated $Sym (\\mathbb N)$-invariant ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Eudes Antonio da Costa","submitted_at":"2013-10-28T20:17:56Z","abstract_excerpt":"Let $K$ be a field and let $\\mathbb N = \\{1,2, \\dots \\}$. Let $R_n=K[x_{ij} \\mid 1\\le i\\le n, j\\in \\mathbb N]$ be the ring of polynomials in $x_{ij}$ $(1 \\le i \\le n, j \\in \\mathbb N)$ over $K$. Let $S_n = Sym (\\{1,2, \\ldots, n \\})$ and $Sym (\\mathbb N)$ be the groups of the permutations of the sets $\\{1,2,\\dots, n \\}$ and $\\mathbb N$, respectively. Then $S_n$ and $Sym (\\mathbb N)$ act on $R_n$ in a natural way: $\\tau (x_{ij})=x_{\\tau(i)j}$ and $\\sigma (x_{ij})=x_{i\\sigma (j)}$ for all $\\tau \\in S_n$ and $\\sigma \\in Sym(\\mathbb N)$. Let $\\overline{R}_n$ be the subalgebra of the symmetric polyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7608","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"}