Jordan-type derivations on trivial extension algebras

Assume that is a unital algebra over a commutative unital ring R and S is an -bimodule. A trivial extension algebra U×S is defined as an R-algebra with usual operations of R-module × and the multiplication defined by (u1,s1)(u2,s2) = (u1u2,u1s2 + s1u2) for all u1,u2 ,s1,s2 . In this paper, we prove that under certain conditions every Jordan n-derivation δ on U×S can be expressed as δ = d + δ, where d is a derivation and δ is both a singular Jordan derivation and an antiderivation. As applications, we characterize Jordan n-derivations on triangular algebras and generalized matrix algebras.