# On uniform acts over semigroups

## TL;DR

This paper explores the properties of uniform acts over semigroups, establishing conditions for their classification, and characterizes regular monoids that are uniform as right acts over themselves.

## Contribution

It introduces new conditions linking uniform and subdirectly irreducible acts, and characterizes regular monoids that are uniform as right acts.

## Key findings

- Uniform acts with two zeros are subdirectly irreducible.
- Conditions are established to bridge classes of acts.
- Regular monoids are characterized when uniform as right acts.

## Abstract

The paper is devoted to the investigation of uniform notion for acts over semigroups perceived as an overclass of subdirectly irreducible acts. We establish conditions to fill the gap between these classes of acts. Besides we prove that uniform acts with two zeros are subdirectly irreducible. Ultimately we investigate monoids which are uniform as right acts over themselves and we characterize regular ones.