Let R be a ring. A right R-module A is said to be C-flat if the kernel of any epimorphism B→ A
is C-pure in B, ie the induced map Hom (C, B)→ Hom (C, A) is surjective for any cyclic right …

Let R be a ring and M a right R-module. M is called n-FP-projective if Ext 1 (M, N)= 0 for any
right R-module N of FP-injective dimension≤ n, where n is a nonnegative integer or n=∞. ν …

We introduce and study the concepts of weak n-injective and weak n-flat modules in terms of
super finitely presented modules whose projective dimension is at most n, which generalize …

In this article, we introduce the concept of IFP-flat (resp., IFP-injective) modules as nontrivial
generalization of flat (resp., injective) modules. We investigate the properties of these …

By utilizing known characterizations of ${\omega} $-Noetherian rings in terms of injective
modules, we give more characterizations of ${\omega} $-Noetherian rings. More precisely …

Let R be a commutative ring with identity. Denote by w𝒫 w the class of weak w-projective R-
modules and by w𝒫 w⊥ the right orthogonal complement of w𝒫 w. It is shown that (w𝒫 w …

In this paper, we introduce and study regular rings relative to the hereditary torsion theory $
w $(a special case of a well-centered torsion theory over a commutative ring), called $ w …

Recently, de la Rosa and Fuchs (Commentarii Math. Univ. Sancti Pauli 35 (1986), 53–57)
discussed the relationship between the projective dimen-sion and the ha-dimension of a …

Let R be a regular ring of characteristic p> 0. In [4], Hochster showed that the category of
Lyubeznikʼs F R-modules has enough injectives, so that every F R-module has an injective …