Let \(M\) be a monoid and \(K\) be a field, then by a character of \(G\) in \(K\) we mean a monoid-homomorphism\[\chi:M \to K^\ast.\] By trivial character we mean a character such that \(\chi(M)=\{1\}\). We are particularly interested in the linear independence of characters. Functions \(f_i:M \to K……