10 citations · 72 across the 23 of their papers we have counts for
8 papers · 1 filter
On the Image Conjecture for Locally Finite Derivations and -Derivations
Arno van den Essen, Wenhua Zhao
Some cases of the LFED Conjecture, proposed by the second author [Z3], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the…
Images of Ideals under Derivations and -Derivations of Univariate Polynomial Algebras over a Field of Characteristic Zero
Wenhua Zhao
Let be a field of characteristic zero and a free variable. A --derivation of is a -linear map of the form for some -algebra…
The LFED and LNED Conjectures for Laurent Polynomial Algebras
Wenhua Zhao
Let be an integral domain of characteristic zero, commutative free variables, and , i.e., the Laurent polynomial alge…
The Gaussian Moments Conjecture and the Jacobian Conjecture
Harm Derksen, Arno van den Essen, Wenhua Zhao
We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. We also give a counter-exampl…
Mathieu Subspaces of Univariate Polynomial Algebras
Arno van den Essen, Wenhua Zhao
We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical u…
Images of Locally Finite Derivations of Polynomial Algebras in Two Variables
Arno van den Essen, David Wright, Wenhua Zhao
In this paper we show that the image of any locally finite -derivation of the polynomial algebra in two variables over a field of characteristic zero is a Mathieu…
A Deformation of Commutative Polynomial Algebras in Even Numbers of Variables
Wenhua Zhao
We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the g…
Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients
Arno van den Essen, Roel Willems, Wenhua Zhao
In this paper we prove four cases of the vanishing conjecture of differential operators with constant coefficients and also a conjecture on the Laurent polynomials with no holomorp…