6 papers
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…
On sums and products of diagonalizable matrices over division rings
Tran Nam Son
This paper aims to continue the studies initiated by Botha in [Linear Algebra Appl. 273 (1998), 65-82; Linear Algebra Appl. 286 (1999), 37-44; Linear Algebra Appl. 315 (2000), 1-23…
Images of polynomial maps and the Ax-Grothendieck theorem over algebraically closed division rings
Elad Paran, Tran Nam Son
We study the images of polynomial maps over algebraically closed division rings. Our first result generalizes the classical Ax-Grothendieck theorem: We show that if $ f_1, \ldots,…
The weak Lefschetz properties of artinian monomial algebras associated to certain tadpole graphs
Phan Minh Hung, Nguyen Duy Phuoc, Tran Nguyen Thanh Son
Given a simple graph , the artinian monomial algebra associated to , denoted by , is defined by the edge ideal of and the squares of the variables. In this article,…
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…