Definition:Degree of Polynomial/Null Polynomial

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

Let $\left({S, +, \circ}\right)$ be a subring of $R$.

For arbitrary $x \in R$, let $S \left[{x}\right]$ be the set $S \left[{x}\right]$ be the set of polynomials in $x$ over $S$.

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

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