零积决定的矩阵代数  

ZERO PRODUCT DERMINED MATRIX ALGEBRAS

作　　者：葛徽[1] 王登银[1] 李小微[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《数学杂志》2013年第4期665-670,共6页Journal of Mathematics

摘　　要：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.

关 键 词：零积决定的代数 零积决定的Jordan代数 零积决定的Lie代数 双线性映射 

分 类 号：O151.2[理学—数学]