Definition:Degree of Polynomial/Null Polynomial/Integral Domain

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Definition

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

Let $\left({D, +, \circ}\right)$ be an integral subdomain of $R$.

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


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


Also defined as

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


Sources