{"paper":{"title":"A slight generalization of Keller's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Vered Moskowicz","submitted_at":"2015-09-21T19:59:12Z","abstract_excerpt":"The famous Jacobian problem asks: Is a morphism $f:\\mathbb{C}[x,y]\\to \\mathbb{C}[x,y]$ having an invertible Jacobian, invertible? If we add the assumption that $\\mathbb{C}(f(x),f(y))=\\mathbb{C}(x,y)$, then $f$ is invertible; this result is due to O. H. Keller (1939). We suggest the following slight generalization of Keller's theorem: If $f:\\mathbb{C}[x,y]\\to \\mathbb{C}[x,y]$ is a morphism having an invertible Jacobian, and if there exist $n \\geq 1$, $a \\in \\mathbb{C}(f(x),f(y))^*$ and $b \\in \\mathbb{C}(f(x),f(y))$ such that $(ax +b)^n \\in \\mathbb{C}(f(x),f(y))$, then $f$ is invertible. A simil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06362","kind":"arxiv","version":2},"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"}