Some remarks on nonnil-coherent rings and $ϕ$-IF rings

Some Remarks on $ϕ$-Dedekind rings and $ϕ$-Prufer rings

In this paper, the notions of nonnil-injective modules and nonnil-FP-injective modules are introduced and studied. Especially, we show that a $ϕ$-ring $R$ is an integral domain if and only if any nonnil-injective (resp., nonnil-FP-injective) module $R$-module is injective (resp., FP-injective). Some new characterizations of $ϕ$-von Neumann regular rings, nonnil-Notherian rings and nonnil-coherent rings are given. We finally characterize $ϕ$-Dedekind rings and $ϕ$-\Prufer\ rings in terms of $ϕ$-flat modules, nonnil-injective modules and nonnil-FP-injective modules.

关于$u$-$S$-Noetherian和$u$-$S$-coherent环的一些注记

Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings

本文研究了$u$-$S$-Noetherian和$u$-$S$-coherent环的特征化问题，并对Bouziri提出的问题给出了否定回答。

关于几乎投射模的两点注记

Two remarks on Almost Projective Modules

本文研究交换环上的几乎投射模，证明了其均为投射模当且仅当环半局部，并给出每个模有几乎投射包络的充要条件为环凝聚且局部阿尔廷，且条件不可省略。