id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4262	Khumprapussorn, Thawatchai	On φ-β-Absorbing Submodules	2022	7	.pdf	application/pdf	3629	275	89	In [2], a proper submodule P of a left R-module M is called β-absorbing if for any element r, s ∈ R and m ∈ M such that rsm ∈ P , we have rs + rs ∈ (P : M) or r(m + m) ∈ P or s(m + m) ∈ P . We recall that a proper submodule P of a left R-module M is called a prime submodule of M if for every r ∈ R and m ∈ M , rm ∈ P implies that m ∈ P or r ∈ (P : M).	cache/ejpam-4262.pdf	txt/ejpam-4262.txt