关于n-纯同调维数的注记  

Notes on n -pure homological dimensions

作　　者：吕家凤[1] 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)

机构地区：[1]浙江师范大学数学科学学院,浙江金华321004 [2]浙江师范大学初阳学院,浙江金华321004

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)。

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.

关 键 词：n-纯正合列 n-纯投射模 n-纯内射模 同调维数 

分 类 号：O153[理学—数学]