This paper provides the several homological characterization of perfect rings and semi-
simple rings in terms of semi-projective modules. We investigate whether Hopkins–Levitzki …

Let R be a ring and 𝑆 be a class of some finitely generated left R-modules. Then a left R-
module M is called 𝑆-projective if for every homomorphism f: S→ M, where S∈ 𝑆, there exist …

Under study are the dual automorphism-invariant modules and pseudoprojective modules.
Some conditions were found under which the dual automorphism-invariant module over a …

Let R be associative ring with unit element and X be unitary right R-module. In this work, we
introduce the definition of the concept small-essentially pseudo injective module (shortly, S …

The study of pure-projectivity is accessed from an alternative point of view. Given modules M
and N, M is said to be N-pure-subprojective if for every pure epimorphism g: B → N g: B→ N …

Let V be a submodule of a direct sum of some elements in U, and X be a submodule of a
direct sum of some elements in N, where U and N are families of R-modules. A U-free …

In this thesis, we will study the relations between weakly injective, weakly projective versus
extending and lifting modules and its generalization. Mainly, we study rings over which …

A module M is called N-almost-invariant for a module N if, for any homomorphism α: F→ E,
either α (N)⊆ M, or there exist nonzero direct summands F′ of F and E′ of E such that α …

Let R be a ring. We have studied rings whose projective modules have the extending
property of simple modules in [3] and [5]. In this note, we shall further study those rings when …