In this paper, we provide a classification of arithmetic functions in terms of identically-free-distributedness, determined by a fixed prime. We show then such classifications are free from the choice of primes. In particular, we obtain that the algeb...
In this paper, we provide a classification of arithmetic functions in terms of identically-free-distributedness, determined by a fixed prime. We show then such classifications are free from the choice of primes. In particular, we obtain that the algebra $A_p$ of equivalence classes under the quotient on A by the identically-free-distributedness is isomorphic to an algebra $\mathbb{C}^2$, having its multiplication $({\bullet});(t_1,t_2){\bullet}(s_1,s_2)=(t_1s_1,t_1s_2+t_2s_1)$.