C-FP-內射维数与C-平坦维数有限的模类

Finite-dimension C-FP-injective and C-flat modules

设R是交换环,n是非负整数.令FI≤nC(F≤nC)是C-FP-內射维数(C-平坦维数)不超过n的模类.证明当R是凝聚环且FP-idR(R)≤n时,(FI≤nC,FI≤nC⊥)是AC(R)中完全遗传的余挠对.给出F≤nC-预包络和FI≤nC-预覆盖的一些刻画.

Let R be a commutative ring,n a non-negative integer and Ff≤Cn（F≤Cn） the C-FP-injective（C- flat） modules with dimension equal to or less than n. In this paper we proved that （Ff≤Cn,Ff≤Cn⊥） would be a perfect hereditary cotorsion pair in AC （R） whenever R were a coherent ring with FP-idR （R）≤n. Meantime, Some characterizations of F≤Cn-preenvelope and Ff≤Cn-precover were given.