Definition:Completely Additive Function

Definition
Let $\struct {R, +, \times}$ be a ring.

Let $f: R \to R$ be a mapping on $R$.

Then $f$ is described as completely additive :


 * $\forall m, n \in R: \map f {m \times n} = \map f m + \map f n$

That is, a completely additive function is one where the value of a product of two numbers equals the sum of the value of each one individually.

Also see

 * Real Logarithm is Completely Additive
 * Completely Additive Function is Additive