Definition:Big Monoid Ring

Definition
Let $\struct {M, \cdot}$ be a divisor-finite monoid.

Let $\struct {R, +, \times}$ be an additive semiring.

The big monoid ring of $R$ over $M$ is the ringoid $\struct {R^M, +, *}$ where:
 * $R^M$ be the set of all mappings $M \to R$
 * $+$ is the pointwise operation induced by $+$
 * $*$ denotes convolution of mappings

Also known as
The big monoid ring is also known as the total algebra of $M$ over $R$.

Also see

 * Definition:Monoid Ring

Examples

 * Definition:Ring of Formal Power Series