Exploring Functional Identities: From Division Rings to Matrix Algebras

Abstract: In this paper, we tackle unresolved inquiries by Ferreira et al. \cite{bruno} in their recent publication, ``Functional Identity on Division Algebras". We delve into the intricate behavior of additive functions on matrix algebras over division rings through rigorous analysis and theorem-proving. Our findings offer valuable insights into the nature of these functions and their implications for algebraic structures.