id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5930	Iampan, Aiyared; Vennila, R. ; Rajesh, Neelamegarajan ; Subasini, Ramasamy 	A Theoretical Exploration of Rough Approximations in Hilbert Algebras	2025	11	.pdf	application/pdf	5065	347	79	b ∈ I ⊆ S. Since a, b ∈ S and S is an ideal of A, we have y1 ∈ S and y2 ∈ S and (y1 · (y2 · x)) · x ∈ S. Note that (y1 · (y2 · x)) · x ∈ I(y1·(y2·x))·x, thus (y1 · (y2 · x)) · x ∈ I(y1·(y2·x))·x ∩ S, that is, I(y1·(y2·x))·x ∩ S ̸= ∅. Hence, (y1 · (y2 · x)) · x ∈ Θ(I, S) and therefore, Θ(I, S) is an ideal of A. (2) Let S be an ideal of A containing I. Let x ∈ I1. Ip, y ∈ Iq, x ∈ S, and y ∈ T .	cache/ejpam-5930.pdf	txt/ejpam-5930.txt