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 …

Let R be a ring and m, n two fixed positive integers. In this article, R is defined to be left
slightly (m, n)-coherent if each n-generated submodule of the left R-module Rm is (m, 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 …

Let R be a ring. A right R-module M is called f-projective if Ext1 (M, N)= 0 for any f-injective
right R-module N. We prove that (F-proj, F-inj) is a complete cotorsion theory, where F-proj …

Let R be a left coherent ring. We first prove that a right R-module M is strongly copure flat if
and only if Ext i (M, C)= 0 for all flat cotorsion right R-modules C and i≥ 1. Then we define …

Let R be a left Noetherian ring, S a right Noetherian ring and RU a generalized tilting
module with S= End (RU). We give some equivalent conditions that the injective dimension …

In this paper we show that if R is a ring of Krull dimension d and M is a strongly copure flat
(respectively, strongly copure injective) module, then E⊗ RM (respectively, HomR (E, M)) is …

For a left Noetherian ring R, if the supremum of flat dimensions of all injective left R-modules
is finite, we prove that strongly cotorsion left R-modules coincide with Gorenstein injective …

Let $ R $ be a ring, and $ n $ a fixed nonnegative integer. An $ R $-module $ W $ is called $
L_ {n} $-injective if ${\rm Ext} _ {R}^{1}(M, W)= 0$ for any $ R $-module $ M $ with flat …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …