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

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9 papers · 1 filter

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.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.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…

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

A Family of Maximal Mathieu Subspaces of Matrix 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

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

On the Image Conjecture

Mathieu Subspaces of Associative Algebras

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