We introduce and study the concepts of weak n-injective and weak n-flat modules in terms of
super finitely presented modules whose projective dimension is at most n, which generalize …

Some of the most familiar cotorsion and Tor pairs on integral domains do not extend to rings
R with divisors of zero. A closer look shows that for some of them the validity hinges on the …

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 …

In basic homological algebra, the flat and injective dimensions of modules play an important
and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions …

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 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 …

Let $ A $, $ B $ be two rings and $ T=\left (\begin {smallmatrix} A & M 0 & B\end
{smallmatrix}\right) $ with $ M $ an $ A $-$ B $-bimodule. Given two complete hereditary …

We study, in this article, the FGT-injective dimensions of Π-coherent rings. If R is right Π-
coherent, and TI (resp. TF) stands for the class of FGT-injective (resp. FGT-flat) R-modules …

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 paper we study the class of FI-cotorsion modules and we introduce there dimensions
of modules and rings. An R-module M is called FI-cotorsion if Ext 1 R (F, M)= 0 for any FI-flat …