Bulletin of the
Korean Mathematical Society BKMS

In this paper, we prove that a ring $R$ is $n$-coherent and self-strongly $FP_n$-injective if and only if $(\mathcal{SFI}_n,\mathcal{SFI}_n^\perp)$ is a (perfect) cotorsion pair, if and only if every $R$-module has an epimorphic $\mathcal{SFI}_n$-cover, where $\mathcal{SFI}_n$ denotes the class of strongly $FP_n$-injective modules. In particular, we show that $R$ is a coherent and self-strongly $FP$-injective ring, if and only if every $R$-module has an epimorphic $\mathcal{SFI}$-cover, which gives an affirmative answer to the question raised by Li-Guan-Ouyang.

Keywords: $n$-coherent ring, $n$-presented module, strongly $FP_n$-injective module, strongly $FP_n$-injective cover

MSC numbers: Primary 13D10,16E05,16E30,16P70

Supported by: This work was financially supported by NSFC(12001384) and NSFC(11401493).