id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-3112	Kareem, Fatema. F. ; Samy M. Mostafa; A. Hasan , Omniat. 	Cubic Of Positive Implicative Ideals In KU- Semigroup	2024	10	.pdf	application/pdf	4176	326	85	Then for all ς,ω, κ ∈ Ν: (1) If ς ≤ ω implyω ∗ κ ≤ ς ∗ κ. (2) ς ∗ (ω ∗ κ) = ω ∗ (ς ∗ κ). Since Θ is a cubic ideal of Ν, then 𝜇Θ(κ ∗ ω) ≥ 𝑟𝑚𝑖𝑛{𝜇Θ((κ ∗ ς) ∗ (κ ∗ ω)) , 𝜇Θ(κ ∗ ς)} and by above condition, we have 𝜇Θ(κ ∗ ω) ≥ 𝑟𝑚𝑖𝑛{𝜇Θ(κ ∗ (ς ∗ ω)) , 𝜇Θ(κ ∗ ς)} , also 𝜆Θ(κ ∗ ω) ≤ 𝑚𝑎𝑥{𝜆Θ((κ ∗ ς) ∗ (κ ∗ ω)) , 𝜆Θ(κ ∗ ς)} and by above condition, we have 𝜆Θ(κ ∗ ω) ≤ 𝑚𝑎𝑥{𝜆Θ(κ ∗ (ς ∗ ω)) , 𝜆Θ(κ ∗ ς)}, which is 𝑪𝒑𝟐, the conditions 𝑪𝒑𝟏 and 𝑪𝒑𝟑 are verify from Definition(10).	cache/iajs-3112.pdf	txt/iajs-3112.txt