Definition:Polynomial Ring/Monoid Ring on Free Monoid on Set
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Definition
Let $R$ be a commutative ring with unity.
Let $I$ be a set.
Let $R \sqbrk {\family {X_i: i \in I} }$ be the ring of polynomial forms in $\family {X_i: i \in I}$.
The polynomial ring in $I$ indeterminates over $R$ is the ordered triple $\struct {\struct {A, +, \circ}, \iota, \family {X_i: i \in I} }$
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