Recall that a left module A (resp. right module B) is said to be singly injective (resp. singly
flat) if Ext^ 1 _ R (F/K, A)= 0 E xt R 1 (F/K, A)= 0 (resp. Tor _ 1^ R (B, F/K)= 0 Tor 1 R (B, F/K) …

Let R be a ring. A left R-module M (resp., right R-module N) is called weak injective (resp.,
weak flat) if (resp.,) for every super finitely presented left R-module F. By replacing finitely …

In this short paper, the homological functors are used to show that a simple module is flat if
and only if it is injective. It is used to give a characterization of Von Neumann regular ring …

Let R be a ring. A left R-module M (resp. right R-module N) is called singly injective (resp.
singly flat) if Ext1 (F/C, M)= 0 (resp. Tor1 (N, F/C)= 0) for any cyclic submodule C of any …

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 …

We introduce the concepts of (n, d)-injective and (n, d)-flat as generalizations of injective, flat
modules and homological dimensions, and use them to characterize right n-coherent rings …

Let R be a commutative ring, and let C be a semidualizing R-module. We introduce the
notion of finitely presented C-injective modules, finitely presented C-flat modules, weak C …

In this paper, we introduced two concepts. A module M is said to be purely quasi-injective
(resp. quasi-cotorsion) if it is fully invariant in its pure-injective envelope (resp. if it is flat and …

In this paper, 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 …

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) …