Almost projective and almost injective modules

TL;DR

This paper characterizes rings where all right modules are almost injective and all simple modules are almost projective, providing structural insights into these classes of modules.

Contribution

It offers a detailed description of rings with the property that every right module is almost injective and every simple module is almost projective.

Findings

Rings where every right module is almost injective are characterized.

Rings with all simple modules almost projective are described.

Structural properties of such rings are elucidated.

Abstract

We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.