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关于n-纯同调维数的注记

Notes on n -pure homological dimensions
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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
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