Let R be a commutative ring, 𝒞 be a semidualizing R-module. We show that the Auslander
class 𝒜𝒞 (R) with respect to 𝒞 is the first left orthogonal class of some pure injective module …

We describe the structure of finitely generated cotorsion modules over commutative
noetherian rings. Also we characterize the so-called covering morphisms between finitely …

In this article, the notion of pure hereditary rings is introduced as a nontrivial generalization
of the notion of both pure semisimple rings and of hereditary rings. Some properties and …

Let R be a ring. A right R-module C is called a cotorsion module if Ext1R (F, C)= 0 for any flat
right R-module F. In this paper, we first characterize those rings satisfying the condition that …

Let R be a ring, M a right R-module, and na fixed non-negative integer. M is called n-
cotorsion if for any flat right R-module N. M is said to be n-flat if for any n-cotorsion right R …

Let R be a ring, na fixed nonnegative integer and FP n (F n) the class of all left (right) R-
modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module …

We apply the theory of cotorsion pairs to study closure properties of classes of modules with
finite projective dimension with respect to direct limit operations and to filtrations. We also …

In this paper we consider the class $\mathcal {P} _1 (R) $ of modules of projective
dimension at most one over a commutative ring $ R $ and we investigate when $\mathcal …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …