几乎弱稳定秩的环  

Ring of Almost Weakly Stable Range

作　　者：郑丽翠[1] 刘伟俊[1] 李冬梅[2] 

机构地区：[1]中南大学数学与统计学院,湖南长沙410083 [2]湖南科技大学数学与计算科学学院,湖南湘潭411201

出　　处：《数学的实践与认识》2015年第10期275-280,共6页Mathematics in Practice and Theory

基　　金：中南大学中央高校基本科研业务费专项资金资助(2013zzts008);国家自然科学基金(11271208;11471108;11426101);湖南省自然科学基金(14JJ6027;2015JJ2051)

摘　　要：主要是介绍了非交换环的几乎弱稳定秩的概念,并利用它来研究非交换环上的右Hermite环,右Bezout环及初等因子环之间的关系.证明了具有几乎弱稳定秩的满足条件V的右(左)Hermite环是初等因子环;还证明了具有几乎弱稳定秩的满足条件V的右Bezout环是右Hermite环;除此之外还得到了几乎的Exchang环具有几乎弱稳定秩.最后,给出了在具有几乎弱稳定秩且J(R)不为零的右(左)Hermite环上的任意矩阵都可以分解成LUM的乘积,其中L,M为下三角矩阵,U为上三角矩阵.We introduce the notion of a ring of almost weakly stable range as a generalization of a ring of weakly stable range. We discussed the relationship between the Hermite ring, Bezout ring and Elementary divisor ring on the noncommutative ring, and proved that a distributive right（left） Hermite ring which has almost weakly stable range and satisfy condition V then R is an elementary divisor ring; R has almost weakly stable range and satisfy condition V R is a right Bezout ring then is a right Hermite ring. We introduce the notion of almost exchange ring and show that an almost exchange ring has almost weakly stable range. Besides, we proved that for any matrix A in a right Hermite ring has almost weakly stable range and with nonzero Jacobson radical J（R） can be decomposed to a LUM, where L, M is a lower triangular matrix, and U is a upper triangular matrix.

关 键 词：Hermite环 初等因子环 Bezout环 几乎弱稳定秩 

分 类 号：O153.3[理学—数学]