# Injective and Automorphism-Invariant Non-Singular Modules

## TL;DR

This paper characterizes when automorphism-invariant right non-singular modules are injective, linking this property to the structure of the ring modulo its right Goldie radical.

## Contribution

It establishes a precise condition involving the ring's factor ring being right strongly semiprime for automorphism-invariant non-singular modules to be injective.

## Key findings

- Automorphism-invariant non-singular modules are injective under specific ring conditions.
- The key condition involves the factor ring of the ring with respect to its right Goldie radical.
- The paper provides a characterization connecting module properties to ring-theoretic structure.

## Abstract

Every automorphism-invariant right non-singular $A$-module is injective if and only if the factor ring of the ring $A$ with respect to its right Goldie radical is a right strongly semiprime ring.