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 …

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, $ S $ a multiplicative subset of $ R $. An $ R $-module $ M $ is said to
be $ u $-$ S $-flat ($ u $-always abbreviates uniformly) if $\Tor^ R_1 (M, N) $ is $ u $-$ S …

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 …

nX-Projective Modules, nX-Injective Modules, Cotorsion Theories Page 1 Int. J. Contemp. Math.
Sciences, Vol. 5, 2010, no. 56, 2753 - 2762 n-X-Projective Modules, n-X-Injective Modules …

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 …

In this paper, strongly cotorsion (torsion-free) modules are studied and strongly cotorsion
(torsion-free) dimension is introduced. It is shown that every module has a special SCn …

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 …

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 Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely
generated R-module. It is shown that the R-modules $ Tor_ {i}^{R}(N, M) $ are I-cofinite for …