# Principal filters of some ordered $\Gamma$-semigroups

## Abstract

For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an ordered $\Gamma$-semigroup $M$ is intra-regular if and only if the ideals of $M$ are semiprime and it is left (right) regular and left (right) duo if and only if the left (right) ideals of $M$ are semiprime.

## Downloads

## Published

2016-12-22

## How to Cite

*Armenian Journal of Mathematics*,

*8*(2), 96-103. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/127

## Issue

## Section

Articles