{"paper":{"title":"Rings with trivial FML-invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Daigle","submitted_at":"2018-06-28T02:20:42Z","abstract_excerpt":"Let $k$ be a field of characteristic zero and $B$ a commutative integral domain that is also a finitely generated $k$-algebra. It is well known that if $k$ is algebraically closed and the \"Field Makar-Limanov\" invariant FML$(B)$ is equal to $k$, then $B$ is unirational over $k$. This article shows that, when $k$ is not assumed to be algebraically closed, the condition FML$(B)=k$ implies that there exists a nonempty Zariski-open subset $U$ of Spec$(B)$ with the following property: for each prime ideal $\\mathfrak{p} \\in U$, the $\\kappa(\\mathfrak{p})$-algebra $\\kappa(\\mathfrak{p}) \\otimes_k B$ ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10739","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"}