广义内射模与平坦模

General injective modules and flat modules

利用同调代数的方法,研究强n-FP-内射模和n-FP-平坦模的若干性质和等价刻画.证明了(~⊥sfI_n,sfI_n)是一个完全遗传余挠理论,其中sfI_n表示所有强n-FP-内射模组成的类.结果表明M是n-FP-平坦右R-模当且仅当对偶模M~*=Hom_R(M,R)是强n-FP-内射左R-模.

Using methods of homological algebra,some properties and equivalent characterizations of strongly n-FP-injective modules and n-FP-flat modules are investigated.It is proved that(~⊥sfI_n,sfI_n)is a complete hereditary cotorsion theory,where sfI_n denotes the class of all strongly n-FP-injective modules.The results indicate that Mis n-FP-flat right R-module if and only if the dual module M~*is strongly n-FP-injective left R-module.