An R-module M is called strongly FP-injective if Ext R i (P, M)= 0 for any finitely presented R-
module P and any i> 0. Denoted by SFI the class of all strongly FP-injective R-modules and …

ABSTRACT A module M is called strongly FP-injective if Ext i (P, M)= 0 for any finitely
presented module P and all i≥ 1.(Pre) envelopes and (pre) covers by strongly FP-injective …

The structure of cyclically pure injective modules over a commutative ring R is investigated
and several characterizations for them are presented. In particular, we prove that a module …

Let R be a commutative Noetherian ring, I an ideal of R, and M an arbitrary R-module. It is
shown that the R-module is finitely generated, for all i≥ 0, if and only if the R-module is …

In this paper, the notions of f-injective and f*-injective modules are introduced. Elementary
properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct …

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective in case every right R-homomorphism from an n-generated submodule of Rm to M …

In this paper, we study the class of complexes of FP-injective left R-modules. It is shown that
the pair is a complete cotorsion pair. If R is a left coherent ring, it is proved that every …

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 …

There are many results of a homological nature which may be generalized from Noetherian
rings to coherent rings. In this process, finitely generated modules should in general be …

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 …