Let R be a ring. Recall that a left R-module M is coherent if every finitely generated
submodule of M is finitely presented. R is a left coherent ring if the left R-module RR is …

In this paper, we introduce a new generalization of coherent rings. Let m be a positive
integer and da positive integer or d=∞. A ring R is called a left (m, d)-coherent ring in case …

The notion of simple-direct-injective modules which are a generalization of injective
modules unifies $ C2 $ and $ C3 $-modules. In the present paper, we introduce the notion of …

R (finitely cogenerated) injective cogenerator in the category of right R-modules. The ring R
is a QF-ring if it is right PF and right (or left) artinian, and in this case R is two-sided PF and …

Recall that a ring R is said to be left coherent [2] if every finitely generated left ideal of R is
finitely presented. Coherent rings and their generalizations have been studied extensively …

In (l), rings whose cyclic left R-modules not isomorphic to R are injective (called left PCI-
rings) are considered. A left R-module M is called CF-injective if for any finitely generated left …

Recently, Costa [4] introduced the concept of n-coherent rings. In this note we shall give
some further properties of n-coherent rings. Let R be a ring and na nonnegative integer …

In this paper, we introduce the notion of c-co-epi-retractable modules. An R-module M is
called c-co-epi-retractable if it contains a copy of its factor module by a complement …

Abstract In (n, d)-ring and n-coherent ring theory, n-presented modules plays an important
role. In this paper, we firstly give some new characterizations of n-presented modules and n …

Given a positive integer n, a left R-module M is called n-coherent (resp. n-semihereditary) if
every n-generated submodule of M is finitely presented (resp. projective). We investigate the …