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第n根性质与根环
引用本文:卢丹诚,吴俊,佟文廷.第n根性质与根环[J].数学杂志,2004,24(2):187-192.
作者姓名:卢丹诚  吴俊  佟文廷
作者单位:南京大学数学系,江苏,南京,210093
基金项目:SupportedbytheNationalScienceFoundationofChina(No :1 0 0 71 0 35 )
摘    要:令E为 (MR)的自同态环 ,本文首先证明了MR 有第n根性质的充要条件是EE 有第n根性质 ,由此引进了根环的概念 ,并研究了根环的性质。特别地我们证明了如nA nB且A拟内射 ,则A B .

关 键 词:根环  第n-性质  正则右自内射环  替代环  n-拟相似性

THE n-TH ROOT PROPERTY AND ROOT RINGS
Abstract.THE n-TH ROOT PROPERTY AND ROOT RINGS[J].Journal of Mathematics,2004,24(2):187-192.
Authors:Abstract
Abstract:Denote End (MR) by E, it is proved that MR has the n-th root property if and only if EE has the n-th root property, which introduces the concept of root rings. We investigate the property of root rings, and give several examples of root rings and modules with the n-th root property. In particular, it is proved that every quasi-injective module has the n-th root property for any n, that is, if nA≌nB and A is quasi-injective, then A≌B.
Keywords:regular right self\|injective ring  exchange ring  n    th root property  n    pseudo similarity  root ring
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