Definition:Big Monoid Ring
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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
Examples
Sources
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