ON GENERALIZED JORDAN DERIVATIONS OF GENERALIZED MATRIX ALGEBRAS

Abstract

Let R be a commutative ring with unity, A and B be Ralgebras, M be a (A,B)-bimodule and N be a (B,A)-bimodule. The Ralgebra S = S(A,M,N,B) is a generalized matrix algebra defined by the Morita context (A,B,M,N, ξMN,ΩNM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.