Definition:Null Polynomial/Polynomial Form

Definition
Let $f = a_1 \mathbf X^{k_1} + \cdots + a_r \mathbf X^{k_r}$ be a polynomial over $R$ in the indeterminates $\left\{{X_j: j \in J}\right\}$.

For all $i = 1, 2, \ldots, r$, let $a_i = 0$.

Then $f$ is the null polynomial in the indeterminates $\left\{{X_j: j \in J}\right\}$.