Lie centralizing mappings on generalized matrix algebras through two-sided zero products

Let (Formula presented) be a generalized matrix algebra defined by the Morita context (A, B, M, N, ΦMN , ΨNM ) and Z(U) the center of U. In this paper, under some certain conditions on U, we prove that if F : U→U is an additive map satisfying [x, F(y)] = 0 for any x, y ∈ U with xy =0= yx, then F has the form F(x) = λx + τ(x) for all x ∈ U, where λ ∈ Z(U) and τ is an additive map from U into Z(U). Finally as its applications, we characterize Lie centralizer maps and generalized Lie derivations on U. Moreover we prove that the similar conclusions remain valid on full matrix algebras, triangular algebras, upper triangular matrix algebras. © 2025 World Scientific Publishing Company.