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

Let U = [GRAPHICS] be a generalized matrix algebra defined by the Morita context (A, B, M, N, Phi(MN), Psi(NM)) 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 is an element of U with xy = 0 = yx, then F has the form F(x) = lambda x + tau(x) for all x is an element of U, where lambda is an element of Z(U) and tau 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.