Let R be a commutative ring. If the nilpotent radical N il (R) of R is a divided prime ideal, then
R is called a ϕ-ring. In this paper, we first distinguish the classes of nonnil-coherent rings …

In this article, we provide several descriptions of w-coherent rings in terms of modules. We
show that a ring R is w-coherent if and only if every direct product of flat modules is w-flat. To …

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In this paper, we obtain that a commutative ring R is w-coherent if and only if Hom R (M, E) is
w-flat for any absolutely pure w-module M and any injective (w-) module E, if and only if Hom …

In this note, we investigate the notion of $ S $-flat preenvelopes of modules. In particular, we
give an example that a ring $ R $ being coherent does not imply that every $ R $-module …

本文介绍了Gorenstein 内射模的类GI 上的严格的Mittag-Leffler 模, 并用余挠对证明了GI-
投射模在Gorenstein 内射模的类GI 上的严格的Mittag-Leffler 模的一些同调性质. Abstract: In …

We show that an N-complex of modules C is FP-injective if and only if C is N-exact and Z ni
(C) is an FP-injective module for each i= 1, 2,⋯, N and each n∈ Z by virtue of Gaussian …

Let $ R $ be a ring. A morphism $\alpha: X\rightarrow Y $ of left $ R $-modules is called a
finitely phantom morphism if for each morphism ${\beta: F\rightarrow X} $ with $ F $ finitely …

Given an R-module C and a class of R-modules 𝒟 over a commutative ring R, we investigate
the relationship between the existence of 𝒟-envelopes (respectively, 𝒟-covers) and the …

In this paper, we study the conditions under which a module is a strict Mittag–Leffler module
over the class 𝒢 ℐ of Gorenstein injective modules. To this aim, we introduce the notion of 𝒢 …