Definition:Ring of Polynomial Forms

Definition
Let $R$ be a  commutative ring with unity.

Let $I$ be a set

Let $\left\{{X_i: i \in I}\right\}$ be an indexed set.

Let $A = R \left[{\left\{{X_i: i \in I}\right\}}\right]$ be the set of all polynomial forms over $R$ in $\left\{{X_i: i \in I}\right\}$.

Let $+$ and $\circ$ denote the standard addition and multiplication of polynomial forms.

The ring of polynomial forms is the ordered triple $\left( A, +, \circ \right)$.

Also known as
Because the ring of sequences of polynomial forms can be used to construct the polynomial ring over $R$, it may be referred to as a polynomial ring.

Also see

 * Ring of Polynomial Forms is Commutative Ring with Unity
 * Definition:Polynomial Ring