  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.

Rings and Algebras