Department of Mathematics

Let S₁, ⋯ , S_N and R be semigroups. For homomorphisms F: S₁× ⋯ × S_N→ R we derive sufficient conditions for existence and uniqueness of homomorphisms F_n: S_n→ R, n= 1 , ⋯ , N, such that F(s₁, ⋯ , s_N) = F₁(s₁) ⋯ F_N(s_N) for all s₁∈ S₁, ⋯ , s_N∈ S_N.