id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3085	Kehayopulu, Niovi	On ordered hypersemigroups with idempotent ideals, prime and weakly prime ideals	2018	13	.pdf	application/pdf	6696	396	90	Then we have t ≤ u for some u ∈ H ∗{x}∗H and t ≤ v for some v ∈ H ∗ {y} ∗H. Since u ∈ ( H ∗ {x} ) ∗H, we have u ∈ v ◦ b for some v ∈ H ∗ {x}, b ∈ H. Since v ∈ H ∗ {x}, we have v ∈ a ◦ x for some a ∈ H. If A is a left ideal of H, then we have A ⊆ (A ∗ (H ∗ A)] ⊆ (A ∗ A] ⊆ (H ∗ A] ⊆ A, thus (A ∗ A] = A.	cache/ejpam-3085.pdf	txt/ejpam-3085.txt