4 papers
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…
A note on additive commutator groups in certain algebras
Nguyen Thi Thai Ha, Tran Nam Son, Pham Duy Vinh
We study whether a unital associative algebra over a field admits a decomposition of the form where is the center of and denotes t…
Images of Multilinear Polynomials on Generalized Quaternion Algebras
Peter Vassilev Danchev, Truong Huu Dung, Tran Nam Son
The main goal of this paper is to extend [J. Algebra Appl. 20 (2021), 2150074] to generalized quaternion algebras, even when these algebras are not necessarily division rings. More…
Products of Traceless and Semi-Traceless Matrices over Division Rings and their Applications
Peter V. Danchev, Truong Huu Dung, Tran Nam Son
We study the problem when every matrix over a division ring is representable as either the product of traceless matrices or the product of semi-traceless matrices, and also give so…