# Nil extensions of simple regular ordered semigroup

## TL;DR

This paper investigates nil extensions of specific ordered semigroups, providing characterizations and decompositions for these structures, enhancing understanding of their algebraic properties and relationships.

## Contribution

It introduces new characterizations of nil extensions in simple regular, left simple, and right regular ordered semigroups, and describes their semilattice decompositions.

## Key findings

- Characterization of nil extensions in various ordered semigroups
- Complete semilattice decomposition of nil extension semigroups
- Enhanced understanding of algebraic structure of ordered semigroups

## Abstract

In this paper, nil extensions of some special type of ordered semigroups, such as, simple regular ordered semigroups, left simple and right regular ordered semigroup. Moreover, we have characterized complete semilattice decomposition of all ordered semigroups which are nil extension of ordered semigroup.