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 …

A module M is called pseudo-projective if every epimorphism from M to each quotient
module of M can be lifted to an endomorphism of M. In this paper, we study some properties …

M is called a P-coherent (resp. PP) module if its every principal submodule is finitely
presented (resp. projective). M is said to be a Baer module if the annihilator of its every …

Let M and N be two modules. M is called essentially pseudo N-injective if for any essential
submodule A of N, any monomorphism f: A → M f: A→ M can be extended to some g ∈ Hom …

For an arbitrary left R-module M, we denote by F (M) the class of left R-modules F such that
for any exact sequence 0→ A α→ B of left R-modules and any R-homomorphism β: A→ M …

Let $\cal F $ be a left Gabriel topology on a ring $ R $ and $\cal X $ be a special class of left
$ R $-modules (for example, the class of all quasi-continuous left $ R $-modules in $\sigma …

Coherent rings relative to (hereditary) torsion theories have been studied in several papers.
The characterization, given by Cateforis I41, of nonsingular rings with flat maximal quotient …

ABSTRACT A right R-module M is called simple-direct-injective if, whenever, A and B are
simple submodules of M with A≅ B, and B⊆⊕ M, then A⊆⊕ M. Dually, M is called simple …

In this paper, we introduce and study a generalization of coretractable modules. An R-
module M is called coretractable relative to an R-module N if Hom R (M/X, N)≠ 0, for any …

A. Tozaki and the author defined almost relative projective modules in [5], and the author
has given a new concept of almost projective modules in [6]. On the other hand, we know …