相对FI-内射模和相对FI-平坦模

Relative FI-injective and Relative FI-flat Modules

定义了n-FI内射模和n-FI平坦模,讨论了这两类模的一些性质,可以利用这两类模再结合Hom导出函子来研究一些环的维数.得到了如下结果:若R是左凝聚环且FP-id(R R)≤n,则左R-模M是n-FI内射模的充要条件是M是一个内射左R-模和一个reduced n-FI内射左R-模的直和.

In this paper,n-FI-injective and n-FI-flat modules were introduced,whose property was investigated.The modules together with the left derived functions of Hom were used to study the dimension of rings,supposing R to be a left coherent ring and FP-id（R R）≤n.It is shown that a left R-module is n-FI-injective if and only if M is a direct sum of an injective left R-module and a reduced n-FI-injective left R-module.