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. 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. A right R-module C is called cotorsion if for any flat right R-module biF. In
this paper, we first give some results on cotorsion envelopes that are analogous to those on …

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 …

A right R-module M is torsion-free (in the sense of Hattori) if for all r∈ R. The class of torsion-
free modules is a cotilting class if and only if R is a left pp-ring. This paper investigates how …

An additive functor from the category of flat right R‐modules to the category of abelian
groups is continuous if it is isomorphic to a functor of the form−⊗ RM, where M is a left R …

Let R be a ring, na fixed non-negative integer and ℱ ℐ n (ℱ n) the class of all right (left) R-
modules of FP-injective (flat) dimension at most n. We prove that (is a perfect cotorsion …

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 …

Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1
R (G, M)= 0 for any flat R-module G. It is well known that each pure-injective left R-module is …

Let R be a ring and na fixed non-negative integer. In this paper, n-weak cotorsion modules
are introduced and studied. A right R-module N is called n-weak cotorsion module if Ext …