体上保秩1的加法算子  

The Additive Rank-1-preserving Map over a Divisor Ring

作　　者：胡振华[1] 

机构地区：[1]湖南城市学院数学与计算科学系,湖南益阳413000

出　　处：《湖南城市学院学报（自然科学版）》2007年第2期40-42,共3页Journal of Hunan City University:Natural Science

摘　　要：刻划矩阵集之间保不变量的线性算子被称为“线性保持问题”的研究.1993年,M.Omladic和P.Semrl用“加法算子”代替线性算子,得到了复矩阵秩1保持的结果.将该问题的研究引向一般体上矩阵,设R是体,n≥2.用Rn×n表示R上n×n阶矩阵的集合,φ是全矩阵环Rn×n上保秩1的加法满射,通过运用体上矩阵秩的各种性质,研究了?的具体形式.The problem of linear preserving is to study of characterizing the linear operation which preserves some invariant elements between the sets of matrices. In 1993, M.Omladic and ESemrl obtained the result of additive mappings preserving operators of rank one of matrix over a field. In this paper, we extend this problem to the general division ring and obtain the following result by the properties of rank one matrix over a division ring： Let R be a division ring and n ≥2. Let R^n×n be the set of all n×n matrices over R, φbe a additive surjective map from R^n×n to itself which preserves rank-one, we obtained the structure of φ by the properties of the rank of R^n×n.

关 键 词：体 秩 加法算子 

分 类 号：O151.21[理学—数学]