3 papers
math.RA2025
On the injectivity of evaluation maps induced by polynomials on certain algebras
Frank Kutzschebauch, Tran Nam Son, Pham Duy Vin
We explore the injectivity of the evaluation map eva f,A from Am A to A, where A is an associative algebra over a field F, and f is a polynomial in m \ge 1 variables with coefficie…
math.RA2025
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…
math.RA2025
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,…