ON GENERALIZED JORDAN DERIVATIONS OF GENERALIZED MATRIX ALGEBRAS

摘要

Let R be a commutative ring with unity, A and B be R-algebras, M be a (A,B)-bimodule and N be a (B,A)-bimodule. The R-algebra S = S(A,M,N,B) is a generalized matrix algebra defined by the Morita context (A,B,M,N,ξ MN ,? NM ). In this article, we study general-ized 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.