Wen-Hua Zhao

activity

20022022

most citedSome Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients

10 citations · 72 across the 23 of their papers we have counts for

collaborators

24 papers

math.RA2022

Existence of Nonzero Trace-Zero Idempotents in the Group Algebras of Finite Groups

Wenhua Zhao, Dan Yan

Let $G$ be a finite group and $K$ a splitting field of $G$ of characteristic $p > 0$ . Denote by $K G$ the group algebra of $G$ over $K$ and $Z (K G)$ the center of $K G$ . Let $V_{G}$ be th…

math.RA2022

A Family of Maximal Mathieu Subspaces of Matrix Algebras

George F. Seelinger, Wenhua Zhao

Let $F$ be a field. In this note we give a construction for a family of maximal Mathieu subspaces (or Mathieu-Zhao subspaces) of the matrix algebras $M_{n} (F)$ $(n \geq 2)$ . As an appl…

math.AC2017

On the Image Conjecture for Locally Finite Derivations and $E$ -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…

math.AC2017★ 10 cited

Images of Ideals under Derivations and $E$ -Derivations of Univariate Polynomial Algebras over a Field of Characteristic Zero

Wenhua Zhao

Let $K$ be a field of characteristic zero and $x$ a free variable. A $K$ - $E$ -derivation of $K [x]$ is a $K$ -linear map of the form $I - ϕ$ for some $K$ -algebra…

math.AC2017★ 8 cited

The LFED and LNED Conjectures for Laurent Polynomial Algebras

Wenhua Zhao

Let $R$ be an integral domain of characteristic zero, $x = (x_{1}, x_{2}, ..., x_{n})$ $n$ commutative free variables, and $A_{n} := R [x^{- 1}, x]$ , i.e., the Laurent polynomial alge…

math.RA2017★ 1 cited

Idempotents in Intersection of the Kernel and the Image of Locally Finite Derivations and $E$ -derivations

Wenhua Zhao

Let $K$ be a field of characteristic zero, $A$ a $K$ -algebra and $δ$ a $K$ -derivation of $A$ or $K$ - $E$ -derivation of $A$ (i.e., $δ=\operatornam…

math.RA2017

The LNED and LFED Conjectures for Algebraic Algebras

Wenhua Zhao

Let $K$ be a field of characteristic zero and $A$ a $K$ -algebra such that all the $K$ -subalgebras generated by finitely many elements of $A$ are finite dimensiona…

math.RA2017

The Radical of the Kernel of a Certain Differential Operator and Applications to Locally Algebraic Derivations

Wenhua Zhao

Let $R$ be a commutative ring, $A$ an $R$ -algebra (not necessarily commutative) and $V$ an $R$ -subspace or $R$ -submodule of $A$ . By the radical of $V$ we mean the…

math.RA2017★ 2 cited

Some Open Problems on Locally Finite or Locally Nilpotent Derivations and $E$ -Derivations

Wenhua Zhao

Let $R$ be a commutative ring and $A$ an $R$ -algebra. An $R$ - $E$ -derivation of $A$ is an $R$ -linear map of the form $I - ϕ$ for some $R$ -alg…

math.AC2015★ 7 cited

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…

math.AC2010★ 4 cited

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…

math.RA2010★ 4 cited

Analogue of the Duistermaat-van der Kallen Theorem for Group Algebras

Wenhua Zhao, Roel Willems

Let $G$ be a group, $R$ an integral domain, and $V_{G}$ the subspace of the group algebra $R [G]$ consisting of all the elements of $R [G]$ whose coefficient of the identity element $1…

math.RA2010

On the Image Conjecture

Arno van den Essen, David Wright, Wenhua Zhao

The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove variou…

math.RA2010★ 7 cited

Mathieu Subspaces of Associative Algebras

Wenhua Zhao

Motivated by the Mathieu conjecture [Ma], the image conjecture [Z3] and the well-known Jacobian conjecture [K] (see also [BCW] and [E]), the notion of Mathieu subspaces as a natura…

math.RT2010★ 6 cited

A Generalization of Mathieu Subspaces to Modules of Associative Algebras

Wenhua Zhao

We first propose a generalization of the notion of Mathieu subspaces of associative algebras $A$ , which was introduced recently in [Z4] and [Z6], to $A$ -modules $…

math.AC2010★ 1 cited

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 $k$ -derivation of the polynomial algebra $k [x, y]$ in two variables over a field $k$ of characteristic zero is a Mathieu…

math.AG2009★ 4 cited

New Proofs for the Abhyankar-Gurjar Inversion Formula and the Equivalence of the Jacobian Conjecture and the Vanishing Conjecture

Wenhua Zhao

We first give a new proof and also a new formulation for the Abhyankar-Gurjar inversion formula for formal maps of affine spaces. We then use the reformulated Abhyankar-Gurjar form…

math.AC2009

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…

math.AC2009★ 10 cited

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…

math.CV2009★ 8 cited

Generalizations of the Image Conjecture and the Mathieu Conjecture

Wenhua Zhao

We first propose a generalization of the image conjecture [Z3] for the commuting differential operators related with classical orthogonal polynomials. We then show that the non-tri…

math.CV2009

Images of Commuting Differential Operators of Order One with Constant Leading Coefficients

Wenhua Zhao

We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call th…

math.CV2002

Exponential Formulas for the Jacobians and Jacobian Matrices of Analytic Maps

Wenhua Zhao

Let $F = (F_{1}, F_{2}, ... F_{n})$ be an $n$ -tuple of formal power series in $n$ variables of the form $F (z) = z + O (∣ z ∣^{2})$ . It is known that there exists a unique formal differential opera…

math.CV2002

D-log and formal flow for analytic isomorphisms of n-space

David Wright, Wenhua Zhao

Given a formal map $F = (F_{1} ..., F_{n})$ of the form $z + higher$ order terms, we give tree expansion formulas and associated algorithms for the D-Log of F and the formal flow F_t.…

math.AG2002

Some Reductions on Jacobian Problem in Two Variables

Wenhua Zhao

Let $f = (f_{1}, f_{2})$ be a regular sequence of affine curves in $\bC^2$. Under some reduction conditions achieved by composing with some polynomial automorphisms of $\bC^2$, we show t…

Existence of Nonzero Trace-Zero Idempotents in the Group Algebras of Finite Groups

A Family of Maximal Mathieu Subspaces of Matrix Algebras

On the Image Conjecture for Locally Finite Derivations and E-Derivations

Images of Ideals under Derivations and E-Derivations of Univariate Polynomial Algebras over a Field of Characteristic Zero

The LFED and LNED Conjectures for Laurent Polynomial Algebras

Idempotents in Intersection of the Kernel and the Image of Locally Finite Derivations and E-derivations

The LNED and LFED Conjectures for Algebraic Algebras

The Radical of the Kernel of a Certain Differential Operator and Applications to Locally Algebraic Derivations

Some Open Problems on Locally Finite or Locally Nilpotent Derivations and E-Derivations

The Gaussian Moments Conjecture and the Jacobian Conjecture

Mathieu Subspaces of Univariate Polynomial Algebras

Analogue of the Duistermaat-van der Kallen Theorem for Group Algebras

On the Image Conjecture

Mathieu Subspaces of Associative Algebras

A Generalization of Mathieu Subspaces to Modules of Associative Algebras

Images of Locally Finite Derivations of Polynomial Algebras in Two Variables

New Proofs for the Abhyankar-Gurjar Inversion Formula and the Equivalence of the Jacobian Conjecture and the Vanishing Conjecture

A Deformation of Commutative Polynomial Algebras in Even Numbers of Variables

Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients

Generalizations of the Image Conjecture and the Mathieu Conjecture

Images of Commuting Differential Operators of Order One with Constant Leading Coefficients

Exponential Formulas for the Jacobians and Jacobian Matrices of Analytic Maps

D-log and formal flow for analytic isomorphisms of n-space

Some Reductions on Jacobian Problem in Two Variables

On the Image Conjecture for Locally Finite Derivations and $E$ -Derivations

Images of Ideals under Derivations and $E$ -Derivations of Univariate Polynomial Algebras over a Field of Characteristic Zero

Idempotents in Intersection of the Kernel and the Image of Locally Finite Derivations and $E$ -derivations

Some Open Problems on Locally Finite or Locally Nilpotent Derivations and $E$ -Derivations