摘要
为了研究环与模的n-纯同调维数,通过同调的方法,分别给出了n-纯投射模与n-纯内射模的一些新刻画.作为应用,证明了环R的n-纯投射整体维数不超过1的充分必要条件是R的n-纯内射整体维数不超过1,得到了一个环R的n-纯投射整体维数与R的n-纯内射整体维数的对应关系.
In order to study the n-pure homological dimension over modules or rings,some new characterizations of n-pure projective modules and n-pure injective modules were given by applying homological methods.As an application,it was proved that the global dimension of n-pure projective modules over a ring R would be at most 1 if and only if the global dimension of n-pure injective modules over R was at most 1.The correspondence between the global dimension of n-pure projective modules over a ring R and if the global dimension of n-pure injective modules over R was also presented.
作者
吕家凤
金欣怡
LYU Jiafeng;JIN Xinyi(School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China;Chuyang Honors College,Zhejiang Normal University,Jinhua 321004,China)
出处
《浙江师范大学学报(自然科学版)》
2024年第1期14-18,共5页
Journal of Zhejiang Normal University:Natural Sciences
基金
国家自然科学面上资助项目(12171206)。
关键词
n-纯正合列
n-纯投射模
n-纯内射模
同调维数
n-pure exact sequence
n-pure projective module
n-pure injective module
homological dimension