Definition:Monic Polynomial

Definition
Let $R$ be a commutative ring with unity.

Let $f \in R[x]$ be a polynomial in one variable over $R$.

Then $f$ is monic $f$ is nonzero and its leading coefficient is $1$.

Let $\left({R, +, \circ}\right)$ be a ring with unity whose unity is $1_R$.

Let $\left({S, +, \circ}\right)$ be a subring of $R$.

Let $\displaystyle f = \sum_{k \mathop = 0}^n a_k \circ x^k$ be a polynomial in $x$ over $S$.

Then $f$ is a monic polynomial iff its leading coefficient $a_n$ is $1_R$.