Biderivations of the Algebra of Strictly Upper Triangular Matrices over a Commutative Ring

Abstract:

      Let $N_n(R)$ be the algebra consisting of all strictly upper triangular $n\times n$ matrices over a commutative ring $R$ with the identity. An $R$-bilinear map $\phi :N_n(R)\times N_n(R)\longrightarrow N_n(R)$ is called a biderivation if it is a derivation with respect to both arguments. In this paper, we define the notions of central biderivation and extremal biderivation of $N_n(R)$, and prove that any biderivation of $N_n(R)$ can be decomposed as a sum of an inner biderivation, central biderivation and extremal biderivation for $n\geq 5$.