Images of locally finite E-derivations of bivariate polynomial algebras

2022/04/12 by Hongyu Jia, Jia, Hongyu, Xiankun Du +3
Mathematics · Physics and Astronomy · Computer Science · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2204.05800

Abstract

This paper presents an E-derivation analogue of a result on derivations due to van den Essen, Wright and Zhao. We prove that the image of a locally finite K-E-derivation of polynomial algebras in two variables over a field K of characteristic zero is a Mathieu-Zhao subspace. This result together with that of van den Essen, Wright and Zhao confirms the LFED conjecture in the case of polynomial algebras in two variables.

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• Images of Linear Derivations and Linear E-derivations of K[x 1 ,x 2 ,x 3 ]
• The LFED Conjecture for some E-derivations
• The LFED and LNED Conjectures for Laurent Polynomial Algebras
• The images of some simple derivations