矩阵代数上的乘积决定点

Product Determined Points on Matrix Algebras

设B是含单位元的交换环C上的代数,且B含单位元,该文利用代数计算推导的方法,主要讨论了矩阵代数Mn(B)的乘积决定点的情况,并对于一般数域上矩阵代数Mn得到G是Mn的乘积决定点的充要条件是rankG≤n-2。

Let B be an algebra over an unital commutative ring C. By the means of algebraic operation and a- nalysis, we first obtain some product determined points of matrix algebra , then we show that G is a product determined point for the matrix algebra on scalar field if and only if rank Gn-2 in this paper.