Jordan derivations and antiderivations on triangular matrices Original Research Article

We define an antiderivation from an algebra A into an A-bimodule M as a linear map δ:A→M such that δ(ab) = δ(b)a + bδ(a) for all a,bset membership, variantA. The main result states that every Jordan derivation from the algebra of all upper triangular matrices into its bimodule is the sum of a derivation and an antiderivation.