id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3495	Naingue, Lynnel; Vilela, Jocelyn	On Companion B-algebras	2019	12	.pdf	application/pdf	5773	444	88	Then for any x, y, z ∈ X, the following hold: (a) 0� y = y and y � 0 = y; (b) x� y = y ∗ (0 ∗ x); (c) if x ∗ z = y, then x = z � y; (d) � is associative in X; (e) x = (x� y)� (0 ∗ y); (f) if (X, ∗, 0) is commutative, then x� y = x ∗ (0 ∗ y). � y = y ∗ (0 ∗ x) = x ∗ (0 ∗ y) = x ∗ y.	cache/ejpam-3495.pdf	txt/ejpam-3495.txt