# Right subdirectly irreducible completely 0-simple semigroups and uniform acts over rectangular bands

## TL;DR

This paper characterizes right subdirectly irreducible completely 0-simple semigroups, showing they are groups with minimal nontrivial subgroups, and explores the structure of uniform acts over rectangular bands.

## Contribution

It provides a complete characterization of right subdirectly irreducible completely 0-simple semigroups and relates uniform acts to subdirectly irreducible acts over rectangular bands.

## Key findings

- Right subdirectly irreducible completely 0-simple semigroups are groups with least nontrivial subgroups.
- Such semigroups are characterized by nontrivial subgroups with nontrivial intersections.
- Uniform acts form an overclass of subdirectly irreducible acts over rectangular bands.

## Abstract

The aim of this paper is characterizing right subdirectly irreducible completely 0-simple semigroups. We prove that such semigroups are indeed groups with least nontrivial subgroups. On the other hand we prove that right irreducible completely 0-simple semigroups are groups for which nontrivial subgroups have nontrivial intersection. Ultimately, we characterize the class of uniform acts as an overclass of subdirectly irreducible acts over rectangular bands.