... Fnand a i∈ A 1 ,a i A 2,1≤i≤n,f A 1 A 2( a 1 ,a 1, , a n ,a n)=f A 1 (a 1, ,a n),f A 2 (a 1, ,a n). In general neither A 1nor A 2is embeddable in A 1× A 2, although ... Congruences, and Directly Indecomposable Algebras 61Definition 7.13. If a 1 ,a 2 A and α : A → B is a map we say α separates a 1and a 2if a 1= a 2.The maps αi: A → A i,i ∈ I, separate points ... a i∈ A 1 ,a i A 2, 1≤i ≤n, thenπ1(f A ( a 1 ,a 1, , a n ,a n)) = π1(f A 1 (a 1, ,a n),f A 2 (a 1, ,a n))=f A 1 (a 1, ,a n)=f A 1(π1( a 1 ,a 1), ,π1( a n ,a n)),so...