Definition:Null Polynomial

Definition
Let $A$ be a commutative ring with unity, and additive identity $0_A$.

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

If $a_i = 0$, $i = 1,\ldots, r$ then $f$ is the null polynomial in the indeterminates $\{X_j : j \in J\}$.