A survey of s-unital and locally unital rings

TL;DR

This paper surveys various classes of rings related to unitality, highlighting their differences and inclusion relations through classical results and examples.

Contribution

It compiles and clarifies the relationships among unital, s-unital, locally unital, and idempotent rings, providing a comprehensive overview.

Findings

Strict inclusion relations between ring classes are demonstrated.

Classical examples illustrate differences among ring types.

The survey clarifies the hierarchy of unital-related rings.

Abstract

We gather some classical results and examples that show strict inclusion between the families of unital rings, rings with enough idempotents, rings with sets of local units, locally unital rings, s-unital rings and idempotent rings.