体上矩阵的减序及其性质  

Minus order of matrices over division ring and its properties

作　　者：张炳村[1] 蔡梦[1] 黄礼平[1] 

机构地区：[1]长沙理工大学数学与计算科学学院,湖南长沙410004

出　　处：《湖南文理学院学报（自然科学版）》2013年第2期1-3,共3页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：湖南省教育厅资助重点科研项目(10A002);2012长沙理工大学研究生科研创新项目

摘　　要：定义了体上矩阵减序,将减序推广到任意有单位元的环上矩阵,并对其性质作了一个简明的讨论.应用体上矩阵理论,证明了体上矩阵减序的5个充要条件.The benefit of this definition is that the minus partial order was extended to matrices over any ring with identity element. The properties was discussed concisely for the minus partial order of matrices over a division ring. Applying the theory of matrices over a division ring, 5 sufficient and necessary conditions for the minus partial order of matrix over division ring were proven.

关 键 词：体 矩阵减序 广义逆 

分 类 号：O151.21[理学—数学] O153.1[理学—基础数学]