Tsiu-Kwen Lee

activity

20212026

most citedCertain functional identities on division rings

2 citations · 3 across the 7 of their papers we have counts for

collaborators

9 papers

math.RA2026

On the structural behavior of images of polynomials

Tsiu-Kwen Lee, Tran Nam Son

The study of images of noncommutative polynomials on algebras has attracted considerable attention. We investigate polynomial images and the additive structures they generate in as…

math.RA2025

Lie ideals and derivations of exceptional prime rings

Tsiu-Kwen Lee

A prime ring $R$ with extended centroid $C$ is said to be exceptional if both $char R = 2$ and $dim_{C} R C = 4$ . Herstein characterized additive subgroups $A$ of a nonexcepti…

math.RA2024

Prime rings having nontrivial centralizers of (skew) traces of Lie ideals

Tsiu-Kwen Lee, Jheng-Huei Lin

Let $R$ be a prime ring with center $Z (R)$ and with involution $*$ . Given an additive subgroup $A$ of $R$ , let $T (A) := {x + x^{*} ∣ x \in A}$ and $K_{0} (A) := {x - x^{*} ∣ x \in A}$ . Let…

math.RA2024

Commutators and products of Lie ideals of prime rings

Tsiu-Kwen Lee, Jheng-Huei Lin

Motivated by some recent results on Lie ideals, it is proved that if $L$ is a Lie ideal of a simple ring $R$ with center $Z (R)$ , then $L \subseteq Z (R)$ , $L = Z (R) a + Z (R)$ for some non…

math.RA2024

Fully noncentral Lie ideals and invariant additive subgroups in rings

Eusebio Gardella, Tsiu-Kwen Lee, Hannes Thiel

We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully nonc…

math.RA2024★ 1 cited

Certain functional identities on division rings of characteristic two

Münevver Pınar Eroğlu, Tsiu-Kwen Lee, Jheng-Huei Lin

Let $D$ be a noncommutative division ring. In a recent paper, Lee and Lin proved that if $char D \neq = 2$ , the only solution of additive maps $f, g$ on $D$ satisfying the ide…

math.RA2024

The $X$ -semiprimeness of Rings

Grigore Călugăreanu, Tsiu-Kwen Lee, Jerzy Matczuk

For a nonempty subset $X$ of a ring $R$ , the ring $R$ is called $X$ -semiprime if, given $a \in R$ , $a X a = 0$ implies $a = 0$ . This provides a proper class of semiprime rings. First, we…

math.RA2024★ 2 cited

Certain functional identities on division rings

Tsiu-Kwen Lee, Jheng-Huei Lin

We study the functional identity $G (x) f (x) = H (x)$ on a division ring $D$ , where $f : D \to D$ is an additive map and $G (X) \neq = 0, H (X)$ are generalized polynomials in the variabl…

math.RA2021

On n-generalized commutators and Lie ideals of rings

Peter V. Danchev, Tsiu-Kwen Lee

Let R be an associative ring.In the paper we study n-generalized commutators of rings and prove that if R is a noncommutative prime ring and n > 2, then every nonzero n-generalized…

On the structural behavior of images of polynomials

Lie ideals and derivations of exceptional prime rings

Prime rings having nontrivial centralizers of (skew) traces of Lie ideals

Commutators and products of Lie ideals of prime rings

Fully noncentral Lie ideals and invariant additive subgroups in rings

Certain functional identities on division rings of characteristic two

The X-semiprimeness of Rings

Certain functional identities on division rings

On n-generalized commutators and Lie ideals of rings

The $X$ -semiprimeness of Rings