id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6792	Anantayasethi, Ananya; Sangsura, Kittisak ; Sarasit, Napaporn 	Direct Product of Q-algebras	2025	10	.pdf	application/pdf	4528	324	83	Since 0i ∈ Xi for all i ∈ I, then (0i)i∈I ∈ ∏ i∈I Xi. Properties (Q1) and (Q2) imply that (0i)i∈I ⊛ (0i)i∈I = (0i)i∈I ∈ S, (ai)i∈I ⊛ (ai)i∈I = (0i)i∈I ∈ S) and (ai)i∈I ⊛ (0i)i∈I = (ai)i∈I ∈ S. Since (ai)i∈I ∈ G( ∏ i∈I Xi), then (0i)i∈I ⊛ (ai)i∈I = (ai)i∈I .	cache/ejpam-6792.pdf	txt/ejpam-6792.txt