id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-1919	Ghawi, Tha'ar Younis	Strongly K-nonsingular Modules	2019	11	.pdf	application/pdf	5787	485	88	Let 𝑀 𝑀 𝑀 be an R-module, where 𝑀 , 𝑀 𝑀. If ∩ is a strongly 𝒦-nonsigular R-module, then both of and is strongly 𝒦-nonsigular. Since 𝑘𝑒𝑟𝜓 ⋬ 𝑀, so 𝑀. 𝑘𝑒𝑟𝜓: 𝑀 ⋬ 𝑀, so by Lemma 15 𝑖𝑖 , 𝑘𝑒𝑟𝜓: 𝑀 ⋬ 𝑅, which hence 𝑘𝑒𝑟𝜑 ⋬ 𝑅, therefore R is strongly 𝒦-nonsigular.	cache/iajs-1919.pdf	txt/iajs-1919.txt