Jordan-type derivations on trivial extension algebras

Assume that U is a unital algebra over a commutative unital ring R and S is an U-bimodule. A trivial extension algebra U (sic) S is defined as an R-algebra with usual operations of R-module U x S and the multiplication defined by (u(1), s(1))(u(2), s(2)) = (u(1)u(2), u(1)s(2) + s(1)u(2)) for all u(1), u(2) is an element of U, s(1), s(2) is an element of S. In this paper, we prove that under certain conditions every Jordan n-derivation Delta on U (sic) S can be expressed as Delta = d + delta, where d is a derivation and delta is both a singular Jordan derivation and an antiderivation. As applications, we characterize Jordan n-derivations on triangular algebras and generalized matrix algebras.