Rings whose ideals are close to automorphism-invariant

TL;DR

This paper investigates rings with ideals that are nearly automorphism-invariant, exploring their structure and relationships with q-rings and Sigma-q-rings, focusing on rings where ideals exhibit automorphism-invariance properties.

Contribution

It introduces new classes of rings characterized by automorphism-invariant ideals and analyzes their connections with q-rings and Sigma-q-rings.

Findings

Rings where every finitely generated right ideal is automorphism-invariant are characterized.

Rings with ideals as finite direct sums of automorphism-invariant ideals are studied.

Connections between these rings, q-rings, and Sigma-q-rings are established.

Abstract

We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of automorphism invariant ideals. Connections between these classes of rings, $q$-ring and $\Sigma$-$q$-rings are also considered