This work aims to contribute to the study of rings in terms of their simple modules. Vast
research has been done in this direction to investigate rings whose simple modules are all …

We consider two types of weak-injectivity domains of a module. Small weak-injectivity
domains gauge the extent of weak injectivity of modules; weak-injectivity domains are an …

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 …

We introduce modules whose injectivity domains are contained in the class of modules with
zero radical and call them working-class. This notion gives a generalization of poor modules …

In this paper, we investigate modules whose elements of their injectivity domains satisfy the
fixed property p. In particular, quasi-poor modules as a generalization of poor modules are …

On rings with one middle class of injectivity domains 1. Introduction Page 1 MATHEMATICAL
COMMUNICATIONS 109 Math. Commun. 27(2022), 109–126 On rings with one middle class …

A ring R is a right SI-ring if every singular right R-module is injective, while R is a right S3I-
ring if every singular semisimple right R-module is injective. In this paper, we investigate and …

We approach the analysis of the extent of the projectivity of modules from a fresh perspective
as we introduce the notion of relative subprojectivity. A module M is said to be N …

ABSTRACT A variety of rings including those that are Morita equivalent to local perfect rings,
two by two upper triangular matrix rings over a division ring or certain rings arising in the …

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