摘要
设R是任何环,n是非负整数,L是R-模.若对任何n-余挠模C,有Ext_R^1(C,L)=0,则L称为C_n-内射模.R是Artin半单环当且仅当每个R-模是C_n-内射模,R是弱整体维数不超过n的环当且仅当每个n-余挠模是C_n-内射模.最后引入C_nI-遗传环,即C_n-内射模的商模还是C_n-内射模的环,并且R是C_nI-遗传环当且仅当R上每个n-余挠模的投射维数不超过1.
Let R be a ring, n be a non-negative integer and L be R-module. For any n-cotorsion module C, if ExtR1 （C,L） = 0, then we call L n-injeetive module. R is a semisimple Artin ring if and only if every R-module is n-injective. R is a ring whose week global dimension is no larger than n if and only if every n-cotortion module is n-injeetive. Finally, we characterize simply the n-hereditary rings, that is, the quotient module of n-injective is still n-injeetive module. Moreover, a ring is n,hereditary if and only if the projective dimension of n-cotorsion modules is no more than 1.
作者
王茜
王芳贵
何可
WANG Xi WANG Fanggui HE Ke(College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan)
出处
《四川师范大学学报（自然科学版）》
CAS
北大核心
2017年第5期588-592,共5页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(11671283)
教育部博士点专项科研基金(20125134110002)
