Definition:Degree of Polynomial/Null Polynomial/Integral Domain
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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 $\text{(a)}$