Definition:Degree of Polynomial/Null Polynomial

Definition
Let $\left({R, +, \circ}\right)$ be a commutative ring with unity whose zero is $0_R$.

Let $\left({D, +, \circ}\right)$ be an integral subdomain of $R$.

Let $X \in R$ be transcendental over $D$.

Let $D \left[{X}\right]$ denote the ring of polynomial forms in $X$ over $D$.

The null polynomial $0_R \in D \left[{X}\right]$ does not have a degree.

Also defined as
Some sources assign the value of $-\infty$ to the degree of the null polynomial.