Remark on quasi-ideals of ordered semigroups

TL;DR

This paper revises and clarifies earlier results on quasi-ideals in ordered semigroups, discusses their properties, and explores similarities between po-semigroups and le-semigroups, contributing to the theoretical understanding of algebraic structures.

Contribution

It corrects previous remarks on quasi-ideals in ordered semigroups and investigates their properties and relationships with other semigroup classes.

Findings

Corrected part of the previous remark on quasi-ideals

Established new results on quasi-ideals in ordered semigroups

Explored similarities between po-semigroups and le-semigroups

Abstract

The aim is to correct part of the Remark 3 of my paper "On regular, intra-regular ordered semigroups" in Pure Math. Appl. (PU.M.A.) 4, no. 4 (1993), 447--461. On this occasion, some further results and the similarity between the $po$-semigroups and the $le$-semigroups is discussed.