2015/05/27 by Vered Moskowicz, Moskowicz, Vered
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.1505.07303
This paper has been withdrawn by the author due to an error in the proof of Theorem 2.1 (since Corollary 9 of Wang may not be applicable here)
openalex publication_date 2015/05/27 · arxiv created 2015/06/17 · arxiv updated 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The famous Jacobian Conjecture asks if a morphism f:K[x,y]→ K[x,y] with invertible Jacobian, is invertible (K is a characteristic zero field). A known result says that if K[f(x),f(y)] ⊆ K[x,y] is an integral extension, then f is invertible. We slightly generalize this known result to the following: If for some "good" λ∈ K (in a sense that will be explained) m K[x,y] ≠ K[x,y] for every maximal ideal m of K[f(x),f(y)][x+ λy], then f is invertible. We also apply our ideas to the Jacobian Conjecture, without any further assumptions.