Definition:Degree of Polynomial/Null Polynomial/Integral Domain

Definition

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

Let $\struct {D, +, \circ}$ be an integral subdomain of $R$.

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

The null polynomial $0_R \in D \sqbrk x$ does not have a degree.

Also defined as

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

Sources

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