In this article, we introduce the concept of IFP-flat (resp., IFP-injective) modules as nontrivial
generalization of flat (resp., injective) modules. We investigate the properties of these …

Let R be a commutative ring and C a semidualizing R-module. For a non-negative integer n,
we study a natural generalization of copure injective (flat) modules by introducing the …

Let R be any ring. We prove that every right R-module is coretractable if and only if R is right
perfect and every right R-module is small coretractable if and only if all torsion theories on R …

In this paper, we introduce the notion of cofinitely injective modules and study their
properties over special types of rings. We define a right R‐module M to be cofinitely injective …

This thesis is consists of five chapter. Chapter 1 is the introduction part of the thesis. In
chapter 2, we present some basic definitions and useful notions. In chapter 3, we study …

Kaplansky [2] proved that if P is a projective module, then every fg submodule of P is
contained in a finitely generated direct summand iff P is the direct sum of fg projectives. We …

Let R be an associative ring with identity, C (R) be the category of complexes of R-modules
and Flat (C (R)) be the class of all flat complexes of R-modules. We show that the flat …

Let (𝒜, ℬ) be a hereditary cotorsion pair in Mod R. We show that the induced cotorsion pair
is complete if and only if the induced cotorsion pair is complete. As applications, some …

In this paper, we show the existence of copure injective preenvelopes over noetherian rings
and copure flat preenvelopes over commutative artinian rings. We use this to characterize …