Definition:Degree of Polynomial/Zero

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

Let $\left({D, +, \circ}\right)$ be an integral domain such that $D$ is a subring of $R$.

Let $x \in R$.

Let $D \left[{x}\right]$ be the ring of polynomials over $x$ in $D$.

A polynomial $f \in D \left[{X}\right]$ in $X$ over $D$ is of degree zero iff $x$ is a non-zero element of $D$, that is, a constant.