id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6190	Leuveras, Jessa Mae; Fuentes, Katrina	Pseudo-Dual B-Algebra	2025	12	.pdf	application/pdf	6275	384	89	Define the binary operations “•” and “∗” on X by x•y = y and x ∗ y = y for all x, y ∈ X. Then the axioms (PDB2) and (PDB3) hold. = [(x • 1) ∗ (x • 1)] ∗ y = 1 ∗ y = y and (x ∗ 1) • (x ∗ y) = [(x ∗ 1) • (x ∗ 1)] • y = 1 • y = y. (iv) By (PDB1) and (PDB3), and (iii), (x•y)∗1 = (x•y)∗(x•x) = [(x • 1) ∗ (x • y)]∗x = y ∗ x and (x ∗ y) • 1	cache/ejpam-6190.pdf	txt/ejpam-6190.txt