交换环上的严格上三角代数上的双导子

Let Nn（R）be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.An R-bilinear map φ ：Nn（R）×Nn（R）→ Nn（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 Nn（R）,and prove that any biderivation of Nn（R）can be decomposed as a sum of an inner biderivation,central biderivation and extremal biderivation for n ≥ 5.

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

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 $n\geq 5$.