id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2513	Sh. Ajeel, Ali; A. Abdulla, Omar; K. Mohammadali, Haibat	Approximaitly Quasi-primary Submodules	2020	10	.pdf	application/pdf	5226	294	85	It follows that either 𝐽𝑄 ⊆ 𝐸: 𝑄 𝑄 𝑠𝑜𝑐 𝑅 𝑄 or 𝐼 𝑄 ⊆ 𝐸: 𝑄 𝑄 𝑠𝑜𝑐 𝑅 𝑄. Since 𝑄 is faithful multiplication then by Lemma (11) 𝑠𝑜𝑐 𝑅 𝑄 𝑠𝑜𝑐 𝑄 , and since 𝑄 is multiplication then 𝐸: 𝑄 𝑄 𝐸 and 𝑟𝑎𝑑 𝐸 𝐸: 𝑄 𝑄. 𝑄 𝑄 𝑠𝑜𝑐 𝑅 𝑄, that is either 𝑠 ∈ 𝐸: 𝑄 𝑠𝑜𝑐 𝑅 or 𝑟 ⊆ 𝐸: 𝑄 𝑠𝑜𝑐 𝑅 ⊆ 𝐸: 𝑄 𝑠𝑜𝑐 𝑅 : 𝑅 .	cache/iajs-2513.pdf	txt/iajs-2513.txt