2022/03/11 by Dan Yan, Yan, Dan
Mathematics · #13C99 #13N15 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2203.05783
openalex publication_date 2022/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper, we study the relation between the images of polynomial derivations and their simplicity. We prove that the images of simple Shamsuddin derivations are not Mathieu-Zhao spaces. In addition, we also show that the images of some simple derivations in dimension three are not Mathieu-Zhao spaces. Thus, we conjecture that the images of simple derivations in dimension greater than one are not Mathieu-Zhao spaces. We also prove that locally nilpotent derivations are not simple in dimension greater than one.