# Minimal bi-ideals in regular and completely regular ordered semigroups

Research paper by Kalyan Hansda

Indexed on: 25 Jan '17Published on: 25 Jan '17Published in: arXiv - Mathematics - Rings and Algebras

#### Abstract

Here we characterize regular and completely regular ordered semigroups by their minimal bi-ideals. A minimal bi-ideal is expressed as a product of a minimal right ideal and a minimal left ideal. Furthermore, we show that every bi-ideal in a completely regular ordered semigroup is minimal and hence a regular ordered semigroup S is completely regular if and only if S is union its of minimal bi-ideals.