零积决定的矩阵代数

ZERO PRODUCT DERMINED MATRIX ALGEBRAS

本文研究了零积决定的矩阵代数A=Mn(B)的条件及分类问题.利用基矩阵及巧妙对线性映射T进行构造和扩充,用初等矩阵的方法.获得了较为简单直接的新的证明(对于文献[1]中一系列的问题),并还对其遗留的问题n=2的情形给予一并解决,推广了文献[1]中的结论.

The present paper investigates the condition and classification of the zero product determined matrix algebra A = Mn （B）. Using the base matrix and a skillfully constructed for the linear mapping T and expansion, by elementary matrix method, a relatively simple and direct method is proposed in order to testify the series of problems mentioned in reference [1]. Moreover, the remaining issues concerning the case of n = 2 is also resolved by using this new method. The conclusions of the reference[1] is promoted.