Let M be a left R-module, AA be a family of some submodules of M and BB be a family of
some left R-modules. In this article, we introduce and characterize A A-coherent, PA PA, FA …

Let $ M $ be a left $ R-$ module and $\pazocal {A}=\{A\} _ {A\in\pazocal {A}} $ be a family of
some submodules of $ M $. It is introduced the classes of (strongly) $ M-\pazocal {A} …

Let $ n, d $ be two non-negative integers. A left $ R $-module $ M $ is called $(n, d) $-
injective, if ${\rm Ext}^{d+ 1}(N, M)= 0$ for every $ n $-presented left $ R $-module $ N $. A …

Let R be a ring, m and n are fixed nonnegative integers, and In the class of all left R-modules
of injective dimension at most n. A left R-module M is called (m, n)-copure injective if Extm+ …

Let R be a ring and I an ideal of R. We define and study I-pure submodules, I-FP-injective
modules, I-flat modules, I-coherent rings and I-semihereditary rings. Using the concepts of I …

We introduce the notion of almost pseudo-injective modules (AP-injective modules), which
generalizes the idea of pseudo-injective and almost injective modules. In support, we …

In this paper, we introduce and study the concept of strongly FI-hollow-lifting modules. As
proper stronger concept of FI-hollow-lifting modules which is a proper generalization of …

Let S and R be rings, SCR be a semidualizing bimodule and n≥ 0 be an integer or n=∞.
We introduce and study C-FP n-injective and C-FP n-flat modules as a common …

In this paper we study M-small principally injective (in short, M-sp-injective) module which is
the generalization of M-principally injective module. We prove that if M is finite dimensional …

Let M be a right R-module. A right R-module N is called small principally M-injective (briefly,
SP-M-injective) if, every R-homomorphism from a small and principal submodule of M to N …