Definition:Ring of Arithmetic Functions

Definition
Let $\mathcal A$ be the set of all arithmetic functions.

Let $*$ denote Dirichlet convolution, and $+$ the pointwise sum of functions.

The ring of arithmetic functions is the ring $\left({\mathcal A, +, *}\right)$.

Also see

 * Ring of Arithmetic Functions is Ring with Unity
 * Definition:Ring of Formal Dirichlet Series