Definition:Polynomial Ring/Notation

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

The embedding $f$ is then implicit.

Also see

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