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

Abstract

Let [Formula: see text] be a generalized matrix algebra defined by the Morita context [Formula: see text] and [Formula: see text] the center of [Formula: see text]. In this paper, under some certain conditions on [Formula: see text], we prove that if [Formula: see text] is an additive map satisfying [Formula: see text] for any [Formula: see text] with [Formula: see text], then [Formula: see text] has the form [Formula: see text] for all [Formula: see text], where [Formula: see text] and [Formula: see text] is an additive map from [Formula: see text] into [Formula: see text]. Finally as its applications, we characterize Lie centralizer maps and generalized Lie derivations on [Formula: see text]. Moreover we prove that the similar conclusions remain valid on full matrix algebras, triangular algebras, upper triangular matrix algebras.