Let A and B be Banach algebras, α,β ∈ Hom(A,B) , α ≤ 1 and β ≤ 1. We define an (α,β) -product on A× B which is a strongly splitting extension of A by B . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.
