Abstract

In this paper, first we obtain the necessary and sufficient condition for an ordered Γ-semihypergroup H to be a relative completely regular 2-duo ordered Γ-semihypergroup for any relative (2, 2)-Γ-hyperideal as well as for any relative (2, 2)-quasi-Γ-hyperideal of H. Then, we find the necessary and sufficient condition that Q = (Q2]S for every relative (2, 2)-Γ-hyperideal Q of H to be a relative quasi-Γ-prime with S ⊆ H. Finally, we prove the necessary and sufficient condition for relative (2, 2)-Γ-hyperideal to be a relative quasi-Γ-prime for a relative completely regular and relative (2, 2)-Γ-hyperideal of H making a chain with inclusive relation.