Let S and R be two associative rings, SCR be a faithfully balanced (S, R)-bimodule. We
introduce and investigate properties of∞-torsionfree modules with respect to SCR, which …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

Let R be a commutative Noetherian ring and C a semidualizing R-module. We obtain an
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …

In this paper we investigate the relationship between strongly torsion-free, maximal Cohen–
Macaulay, and strongly cotorsion modules over Cohen–Macaulay local rings via local …

Given a finite dimensional algebra A over a field k, and a finite acyclic quiver Q, let Λ= A⊗ kk
Q/I, where kQ is the path algebra of Q over k and I is a monomial ideal. This paper is devoted …

Let R be a ring. It is reasonable to use a strict 𝒲𝒳-resolution of a right R-module M of finite 𝒳-
projective dimension, where 𝒳 denotes a subcategory of right R-modules closed under …

We study three triangulated categories associated to a Gorenstein ring, that is, a right-and
left-noetherian ring with finite right and left injective dimension. After a survey of exact …

In this paper, we introduce the concept of NN-torsion-free modules (respectively, NN-
injective modules) as a generalization of nonnil-torsion-free modules (respectively, injective …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …

We study homological and homotopical aspects of Gorenstein flat modules over a ring with
respect to a duality pair $(\mathcal {L, A}) $. These modules are defined as cycles of exact …