Mean behaviour of multiplicative functions on additive arithmetical semigroups

In this paper, the authors prove Chebyshev-type estimates and asymptotic formulae, for the prime elements in general additive arithmetical semigroups. Mean value theorems with remainder term estimates are proved for a large class of multiplicative functions on additive arithmetical semigroups. As applications, the authors derive asymptotic formulae for the mean behavior of prime divisor functions and of distinct degrees of prime factors. The paper continues the investigations of the authorsʹ paper [l].