AbstractLet be a commutative ring with unity, 𝒜, be -algebras, be (𝒜, )-bimodule and 𝒩 be (, 𝒜)-bimodule. The -algebra 𝒢 = 𝒢(𝒜, , 𝒩, ) is a generalized matrix algebra defined by the Morita context (𝒜, , , 𝒩, ξ𝒩, Ω𝒩). In this article, we study Jordan σ-derivations on generalized matrix algebras.
The aim of the paper is to give a description of nonlinear Jordan derivable mappings of a certain class of generalized matrix algebras by Lie product square-zero elements. We prove that under certain conditions, a nonlinear Jordan derivable mapping
Δ
of a generalized matrix algebra by Lie product square-zero elements is a sum of an additive derivation
δ
and an additive antiderivation
f
. Moreover,
δ
and
f
are uniquely determined.
σ-derivations on generalized matrix algebras