Images of Linear Derivations and Linear E-derivations of K[x 1 ,x 2 ,x 3 ]

2021/05/02 by Haifeng Tian, Tian, Haifeng, Xiankun Du +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2105.00386

openalex publication_date 2021/05/02 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28

Abstract

Let K be a field of characteristic zero. We prove that images of a linear K-derivation and a linear K-E-derivation of the ring K[x 1 ,x 2 ,x 3 ] of polynomial in three variables over K are Mathieu-Zhao subspaces, which affirms the LFED conjecture for linear K-derivations and linear K-E-derivations of K[x 1 ,x 2 ,x 3 ].

Citations

• Images of Ideals under Derivations and \mathcal E-Derivations of Univariate Polynomial Algebras over a Field of Characteristic Zero
• Monomial preserving derivations and Mathieu–Zhao subspaces

Related

• The LFED Conjecture for some E-derivations
• Images of Ideals under Derivations and \mathcal E-Derivations of Univariate Polynomial Algebras over a Field of Characteristic Zero
• Images of locally finite E-derivations of bivariate polynomial algebras
• The images of some simple derivations
• Simple derivations and their images