id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-3019	Abdullah, Omer; Karim Mohammadali, Haibat 	Extend Nearly Pseudo Quasi-2-Absorbing submodules(I)	2023	13	.pdf	application/pdf	7707	322	79	Let 𝑉 be a Quasi-2-Absorbing submodule of an Ʀ-𝑚𝑜𝑑𝑢𝑙𝑒 Ѡ and ɑɓ𝑐ӽ ∈ 𝑉, for ɑ,ɓ, 𝑐 ∈ Ʀ, ӽ ∈ Ѡ. Since 𝑉 is Quasi-2-Absorbing submodule of Ѡ, then either ɑ𝑐ӽ ∈ 𝑉 ⊆ 𝑉 + 𝑠𝑜𝑐(Ѡ) + 𝐽(Ѡ) or ɓ𝑐ӽ ∈ 𝑉 ⊆ 𝑉 + 𝑠𝑜𝑐(Ѡ) + 𝐽(Ѡ) or ɑɓӽ ∈ 𝑉 ⊆ 𝑉 + 𝑠𝑜𝑐(Ѡ) + 𝐽(Ѡ), hence either ɑ𝑐ӽ ∈ 𝑉 + 𝑠𝑜𝑐(Ѡ) + 𝐽(Ѡ) or ɓ𝑐ӽ ∈ 𝑉 + 𝑠𝑜𝑐(Ѡ) + 𝐽(Ѡ) or ɑɓӽ ∈ 𝑉 + 𝑠𝑜𝑐(Ѡ) + 𝐽(Ѡ). Let ɑɓ𝑐ӽ ∈ 𝑉, for ɑ,ɓ, 𝑐 ∈ Ʀ, ӽ ∈ Ѡ. That is ɑɓ(𝑐ӽ) ∈ 𝑉. But 𝑉 is Pseudo-2-Absorbing submodule of Ѡ, then either ɑ(𝑐ӽ) ∈ 𝑉 + 𝑠𝑜𝑐(Ѡ) or ɓ(𝑐ӽ) ∈ 𝑉 + 𝑠𝑜𝑐(Ѡ) or ɑɓѠ ⊆ 𝑉 + 𝑠𝑜𝑐(Ѡ).	cache/iajs-3019.pdf	txt/iajs-3019.txt