Definition:Degree of Polynomial

One variable
Let $R$ be a commutative ring with unity.

Let $P \in R \sqbrk x$ be a nonzero polynomial over $R$ in one variable $x$.

The degree of $P$ is the largest natural number $k \in \N$ such that the coefficient of $x^k$ in $P$ is nonzero.

Also known as
The degree of a polynomial $f$ is also sometimes called the order of $f$.

Some sources denote $\map \deg f$ by $\partial f$.