arXiv subjects

Wen-Fong Ke

Publications and source records attributed to Wen-Fong Ke.

6 recordsLinked to original sources

arXiv2025

Commutator products in skew Laurent series division rings

In 1965, Baxter established that a simple ring is either a field or that every one of its elements can be expressed as a sum of products of commutator pairs. In a recent paper, Gardella and Thiel demonstrated that every element in a noncommutative division ring can be represented as the sum of just two products of two commutators. They further posed the question of whether every element in a noncommutative division ring can be represented as the product of two commutators. In this paper, we affirmatively answer this question for skew Laurent series division rings over fields.

math.RA↗

arXiv2024

Are zero-symmetric simple nearrings with identity equiprime?

We show that there exist zero-symmetric simple nearrings with identity which are not equiprime, solving a longstanding open problem.

math.RA↗

arXiv2023

Sequences Derived from The Symmetric Powers of $\{1,2,\ldots,k\}$

For a fixed integer $k$, we define a sequence $A_k=(a_k(n))_{n\geq0}$ and a corresponding sparse subsequence $S_k$ using the cardinality of the $n$-th symmetric power of the set $\{1,2,\ldots, k\}$. For $k\in\{2,\dots,8\}$, we find recursive formulas for $S_k$, and show that the values $a_{k}(0)$, $a_{k}(1)$, and $a_{k}(3)$ are sufficient for constructing $A_{k}$.

math.CO↗

arXiv2023

Overlaps in Field Generated Circular Planar Nearrings

We investigate circular planar nearrings constructed from finite fields as well the complex number field using a multiplicative subgroup of order $k$, and characterize the overlaps of the basic graphs which arise in the associated $2$-designs.

math.CO↗

arXiv2023

Circularity in Finite Fields and Solutions of the Equations $\boldsymbol{x^{m}+y^{m}-z^{m}=1}$

An explicit formula for the number of solutions of the equation in the title is given when a certain condition, depending only on the exponent and the characteristic of the field, holds. This formula improves the one given by the authors in an earlier paper.

math.NT↗

arXiv2016

On Polynomial Rings Over Nil Rings in Several Variables and the Central Closure of Prime Nil Rings

We prove that the ring of polynomials in several commuting indeterminates over a nil ring cannot be homomorphically mapped onto a ring with identity, i.e. it is Brown-McCoy radical. It answers a question posed by Puczylowski and Smoktunowicz. We also show that the central closure of a prime nil ring cannot be a simple ring with identity solving a problem due to Beidar.

math.RA↗