保体上上三角幂等矩阵的诱导映射  

Induced maps preserving upper triangular idempotent matrices over skew fields

作　　者：张隽[1] 付丽[1,2] 曹重光[1] 

机构地区：[1]黑龙江大学数学科学学院,黑龙江哈尔滨150080 [2]绥化学院信息工程学院,黑龙江绥化152061

出　　处：《纯粹数学与应用数学》2015年第6期628-635,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(11371109)

摘　　要：假设T_m(D)是体D上所有上三角m×m矩阵的集合.首先分别给出诱导映射和保幂等性的定义.然后为了刻画T_m(D)的保幂等的诱导映射,提出类序列的概念,同时描述类序列的性质.最后,使用矩阵技术和初等方法,借助于分类讨论得到了T_m(D)的保幂等的诱导映射的一般形式并且给出了某些例子,用以解释某些结果之间的关系.Suppose that Tm(D) is set of all m × m upper triangular matrices over skew field D. First, the paper gives the definition of induced map and preserving idempotence, respectively. And then, in order to characterize induced map preserving idempotence on Tm(D), the paper raises the concept of class-sequence and describes the properties of it. In the end, the paper uses matrix techniques and elementary methods and by classified discussion we get the general forms of induced maps preserving idempotence on Tm(D) and give some examples to illustrate relations between some results.

关 键 词：体 上三角矩阵 保幂等 诱导映射 

分 类 号：O178[理学—数学]