Commutative ring/Coset for ideal/Definition

Let ${\displaystyle {}R}$ be a commutative ring, and let ${\displaystyle {}I\subseteq R}$ be an ideal in ${\displaystyle {}R}$. For ${\displaystyle {}a\in R}$, the subset

${\displaystyle {}a+I={\left\{a+f\mid f\in I\right\}}\,}$

is called the coset of ${\displaystyle {}a}$ to the ideal ${\displaystyle {}I}$. Every subset of this form is called a coset to ${\displaystyle {}I}$.