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

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 …

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 …

Several authors have been interested in cotorsion theories. Among these theories we figure
the pairs $(\mathcal P_n,\mathcal P_n^{\perp}) $, where $\mathcal P_n $ designates the set …

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 …

We have considered the general theme of envelopes and covers of mod ules in Chapter 1
and 2. From now on we will concentrate on fiat covers and the topics closely related to fiat …

Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules Tor i R
(N, M) are I-cofinite for all i≥ 0 if M and N are I-cofinite R-modules and N is of dimension at …

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 …

We show that any finitely generated projective cotorsion left module over a ring of left pure
global dimension at most 1 is a direct sum of indecomposable direct summands. We deduce …

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 …