可换环上矩阵代数的拟导子

Let R be an arbitrary commutative ring with identity. Denote by Mn(R) the associative R¡algebra over R consisting of all n by n matrices. An invertible linear transformation Á on Mn(R) is called a quasi-derivation of it if there exists an invertible linear transformation Á0 on Mn(R) such that Á0(xy) = Á(x)y + xÁ(y) for 8x; y 2 Mn(R). The aim of this paper is to give an explicit description on the quasi-derivations of Mn(R). Generalizes the notion of derivation to a more general case.