# Definition:Degree of Polynomial/Zero

## Definition

Let $\struct {R, +, \circ}$ be a ring whose zero is $0_R$.

Let $\struct {S, +, \circ}$ be a subring of $R$.

For arbitrary $x \in R$, let $S \sqbrk x$ be the set of polynomials in $x$ over $S$.

A polynomial $f \in S \sqbrk x$ in $x$ over $S$ is of **degree zero** if and only if $x$ is a non-zero element of $S$, that is, a constant polynomial.

## Sources

- 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 64$. Polynomial rings over an integral domain: Remarks $\text{(a)}$