Definition:Big Monoid Ring

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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