Generalized Jordan derivations on triangular matrix algebras

Abstract

Abstract In this note, we prove that every generalized Jordan derivation from the algebra of all upper triangular matrices over a commutative ring with identity into its bimodule is the sum of a generalized derivation and an antiderivation. Keywords: Generalized Jordan derivationGeneralized derivationAntiderivationTriangular matrix algebraKeywords: 1991 Mathematics Subject Classifications: 47B4747L35 Acknowledgement This research was supported by the National Natural Science Foundation of China (No. 10571114) and the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2005A1).