n-C-余纯内射(平坦)模（英文）

n-C-copure Injective(Flat)Module

设C是交换环R上的半对偶化模,n是任意一个非负整数.本文引入并研究了由半对偶化模C诱导的n-C-余纯内射(平坦)模.得出它是C-Gorenstein内射(平坦)模的一个推广,当R是一个诺特环并且C的内射维数不大于n时,n-C-余纯内射(平坦)模就是C-Gorenstein内射(平坦)模.最后,本文得出n-C-余纯平坦模类总是一个盖类,当R是诺特环时,n-C-余纯内射模类是一个包类.

Let Rbe a commutative ring and Ca semidualizing R-module.For some non-negative integer n,we introduce and investigate the n-C-copure injective(flat)modules with respect to C,which share many common properties with the C-Gorenstein injective(flat)modules.We show that they are exactly C-Gorenstein injective(flat)modules when the injective dimension of Cis no more than.Moreover,we show the class of n-C-copure flat modules is covering and the class of n-C-copure injective modules is enveloping when Ris a Noetherian ring.