{"paper":{"title":"The two-dimensional Jacobian Conjecture and unique factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Vered Moskowicz","submitted_at":"2016-06-14T19:59:52Z","abstract_excerpt":"The two-dimensional Jacobian Conjecture says that a $\\mathbb{C}$-algebra endomorphism $F:\\mathbb{C}[x,y] \\to \\mathbb{C}[x,y]$ that has an invertible Jacobian is an automorphism. We show that if a $\\mathbb{C}$-algebra endomorphism $F:\\mathbb{C}[x,y] \\to \\mathbb{C}[x,y]$ has an invertible Jacobian and if $v \\in \\mathbb{C}[F(x),F(y),x]$ is a product of prime elements of $\\mathbb{C}[F(x),F(y),x]$, then $F$ is an automorphism, where $v$ is such that $y = u/v$, where $u \\in \\mathbb{C}[F(x),F(y),x]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04531","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"}