Some aspects of quasi-pseudo principally injective modules

TL;DR

This paper introduces and studies the concept of quasi-pseudo principally injective modules, exploring their properties, characterizations, and applications in classifying certain types of rings like Noetherian and Dedekind domains.

Contribution

It defines the new notion of quasi-pseudo principally injective modules and provides characterizations and properties, including applications to ring classification.

Findings

Quasi-pseudo principally injective modules are closed under direct summands.

Characterizations of Noetherian Rings via quasi-pseudo principally injectivity.

Characterizations of Dedekind Domains via quasi-pseudo principally injectivity.

Abstract

In this paper, the notion of quasi-pseudo injectivity relative to a class of submodules, namely, quasi-pseudo principally injective has been studied. This notion is closed under direct summands. Several properties and characterizations have been given. In particular, we characterize Noetherian Rings and Dedekind Domains by quasi-pseudo principally injectivity.