Definition:Polynomial Ring/Notation

Notation
It is common to denote a polynomial ring $\left({S, f, X}\right)$ over $R$ as $R \left[{X}\right]$, where $X$ is the indeterminate of $\left({S, f, X}\right)$.

The embedding $f$ is then implicit.

Also see

 * Polynomial Ring is Generated by Indeterminate over Ground Ring, which justifies the notation $R \left[{X}\right]$.